the only place i can think of where you will get direct flights is Athena [Athens] the holiday season dosn't get started till the 1st of may as for prices capital cities around the world are all expensive just some more than others

yasus
wizard

We have only been to Greece twice never that early so i cant commnet , but we go august , and to be honest with you we found Rhodes and Crete very good value for money , people advise not to go to euro zones but i can honestly say that we found Crete and Rhodes to be cheaper than Turkey , i think you will find Rome to be very expensive , but if its a birthday treat spoil yourself and enjoy

You will find Greece/Athens cheaper than Rome. I go to Athens numerous times a year (got home from there again yesterday) & live in Greece, so if you give an idea of budget for hotels (in euros) etc I will help with suggestions in the best locations for the sights.
There are many historical sites in a small area of Athens, a good selection of museums & other attractions as well.
What are your interests & how long are you planning to come for? When in April? This could make a difference if it's over the Easter holiday, it's the biggest celebration of the year in the Greek Orthodox church, absolutely fantastic to see, but does make a difference to some of the advice.

You can certainly fly to Rhodes in april,most of the charter flights start in the 2nd or 3rd week but it tends to only be the bigger chain hotels that are doing packages with the tour operators before may,also if you try and go at Easter you may find the prices are ridiculous,easter in Greece is bigger than xmas in the UK and prices tend to go up accordingly,that said if you do get a flight and hotel at a good price you'll have an amazing time during Paskha(easter) and you'll eat and drink a LOT!

Remember that easter in Greece is on a different date to everywhere else most years but i think in 2011 it's the same as the UK.

If you want a city break for eating,drinking and shopping then personally i'd go to Thessaloniki,you can direct flights there from the UK on BA,olympic,aegean and some of the charter airlines like thomson as it's the airport that also serves Halkidiki,but if you want to do the ancient sites etc then Athens or Heraklion(crete) is your best bet,just don't get a hotel on omonia square

As for the recession, most things have remained exactly the same throughout as far as tourists are concerned, most of the price hikes that have hit Greece have been for things most tourists wouldn't really notice too much, petrol has gone up as the govt. applied more duty to it and this has had a knock on effect on shop prices for a lot of things but it's negligible for things like eating and drinking out

Glyfada area is fantastic