OK, here goes!
My partner and I are visiting Cuba for a week, end of May and staying in Havana, right in the centre.
Do you mean that you are staying in the Vedado area (which is geographically in pretty much the centre of modern day Havana city), the district known as Centro (which is to the east of the modern geographic centre) or Havana Viejo which is the old colonial centre of the historic city and now on the eastern edge of the city? I'm not trying to be pedantic but it makes a difference to sites of interest are within walking distance and which you'd really need to take a taxi too. If you are staying in Viejo (which is what most tourists tend to regard as the 'centre' of Havana) then nearly everything of historic interest worth seeing in within walking distance.
I brought the Lonely Planet and some other guides, but would appreciate any recommendations on places of particular interest, both foodwise and site wise.
Havana Viejo is one big historic site but the Cathedral is worth the effort as are the 3 main Plazas - just go and soak up the atmosphere over a coffee or a mojito and watch the world go by. All the main museums and the Capitolio itself are located here and worth the time in my view but be prepared for the fact that most of the information on the notices etc is in Spanish only. If you are staying in Viejo it will be worth taking a taxi westwards to the Plaza de la Revolucion and going up to the top of the Marti Monument - even if you have no interest in Cuban history, the panoramic view from the top will help give you your bearings in relation to the city as a whole and of course you'll get the best camera shots of the huge wrought version of the iconic image of Che on one of the modern buildings across the plaze from the memorial!
In the opposite direction, the castle of El Morro is always worth a visit to the east and across the river from Viejo - take a taxi through the tunnel. Best to go in the very late afternoon so that after doing the tour of the castle you can stay on for the sunset ceremony when a cannon is fired and the Cuban flag is lowered - both a bit kitsch and also quite moving at one and the same time.
Even if you aren't into rum and cigars - a trip around the respective factories and museums is interesting. The Partega factory isn't really a factory as we would know them - everything is still done by hand and the workforce has the newspaper read out them in the morning and a novel in the afternoons to counteract the boredom of handrolling cigars all day! And of course there are numerous places to visit with associations with Ernest Hemingway if you are into him.
But best of all, do a 'bar crawl' down Obispo of an evening and have a beer or a cocktail in any or all of the bars where there is a live band playing. You'll hear some of the best latin jazz and dance music going if you do.
As for food, the best food will always be found in 'paladares' small, private restaurants set up in peoples' own homes. They open and close with amazing rapidity and which is best at any one time can be really variable - so what was good last July when I was last in Havana could have gone downhill if it has become really popular and they are struggling to keep up standards or it mightn't even be open now. So it's best to ask around once you arrive. On the whole the food outside of the home isn't much cop - with few exceptions, the best food I've eaten in Cuba has always been in privates homes.
Thinking about renting a car, do they supply sat navs with the car as an optional extra? How good are the roads and signage out there?
You won't find sat nav in Cuba full stop - even if you bring your own you'll have to declare it at Cuban Customs and are likely to find that it will be taken from you. But it's unlikely to be of any use anyway - the thing to remember is that Cuba is still in many ways a 3rd world country and sat nav technology is American technology and hence affected by the US embargo. You can rent small modern European hatchbacks (nearly all rental cars throughout the island are usually Peugots) but they aren't cheap or you can rent a restored American saloon from the 50s but as far as I am concerned the cost is extortionate!
Also, the roads are usually in terrible condition, Cuban drivers take no prisoners and once you are off the main 'motorways' then road signs are few and far between. Generally in Cuba it is cheaper and easier for relatively local journeys and day trips to use a taxi - you can negotiate a 'daily rate' or else ask around and somebody's 'brother' will do the same at a lower rate. Just remeber that if you do this - as far any policemen who stop the car are concerned you are a 'friend of the family' and of course no money has changed hands - in fact keep quiet and leave it up to the driver to deal with.
If you are planning to drive then buy your road maps here before you go - the laminated one I bought from Stanfords here is better than anything I've ever come across there or that is likely to be supplied by with the hire car.
What about trains out there? Any good for getting around?
Don't even think about it! Seriously, the trains are old, unreliable and even the Cubans only use them if they really cannot afford to go by bus. Within the city itself use a taxi (safe and cheap) and for travelling longer distances that are further than is 'taxiable' then use the Viazul buses for travelling between cities but they do need to be booked in advance - you can't just turn up and pay on the bus. You have never met a true bureaucrat until you've encountered a Cuban one! What is offically a 16 hr train journey between Havana and Santiago (the Viazul bus takes 12hrs) actually took a friend nearly 3 days in total from first going to the station to try and book his ticket! And even though he is a reasonably proficient Spanish speaker he still managed to buy the wrong sort of ticket so he couldn't use the buffet on the train. No joke on a 16 hr journey -even worse when you end up on for 36. The one good thing about the frequent breakdowns was that every time it did, local food sellers turned up from nowhere because they can recognise a captive market when they see one.
I'd like to visit the beach, preferably daily inbetween touring and exploring. Is the beach far away from Havana capital?
Simple answer is, yes, the beaches are some distance from the city centre - the best are well to the east of Cojimar and a 15-20 CUC taxi in each direction. The Viazul buses are much cheaper but are infrequent. Those to the west by the suburb of Miramar are nearer but not as nice and still a 10CUc taxi ride away. Havana is not really a good place for trying to combine both a city break and a beach holiday. Given that you are only in Cuba for a week my advice would be not to bother with the beaches local to Havana and if you really want to spend some time on the beach then do an 'overnighter' on one of the cayos the north of the island or even in Varadero.
Not read much about the archipelago islands. Am interested in visiting a few of these and also, don't laugh , the country's only nudist island, can't remember the name of it. Just for a day.
None of the islands/cayos that are worth spending time on are really within day trip distance of Havana. Cuba is a very big island - approximately 1,000 kms from end to end and Havana is in the penultimate region to the western end of the island. The other thing to remember is that most of the cayos are not inhabited - they have been developed specifically as tourist resorts and so you won't see much of local life and the only locals you'll meet are the staff who are there to serve you. For chillout time I can recommend Cayo Levisa as being one of the more accessible from Havana but even so, it's not worth the time you'd spend travelling just for a day out. I can't help you re a nudist island - I've never heard of one in Cuba. Cubans do dress very skimpily at times but are also prudish in some ways as well.
We are keen to get out, explore, meet the locals, eat at places off the beaten track.
If you want to get a feel for local life and culture, meet anybody other than staff employed to do things for you then, given that you will be based in Havana, the best way of doing this is to get out and about on foot around the city, give the cayos a miss, perhaps do an 'overnighter' in Jibacoa for a few days on the beach if that is important to you (it's the nearest resort to Havan with a more Cuban feel) and perhaps best of all, if you haven't already booked into a hotel - stay in a 'casa particulare' as a paying house guest with a family.
I hope that the above is enough for starters but if you have more specific questions then do keep asking.
SM