Assuming Vanuatu, Costa Rico and Hawaii are a bit far for a week, I would suggest Iceland which is highly volcanic - but I believe most, if not all of the roads, to the interior are closed from around end of september so visiting a "live" volcano may not be achievable. Maybe someone else can confirm???

There is a volcanic exhibition in Rejkyavik city where they show films of volcanic activity (the formation of Sertsey etc) and of course areas like the Geysir park and blue lagoon could also (loosely) be classified as volcanic and are accessible all year round being on the coast road.

I would give Sicily a try, I can't see why your friend would try to put you off going there though I know it's not such a popular package holiday destination for British tourists. I would think some tour companies do packages to this destination. I myself have been looking into going there this September/October DIY, I am finding prices more expensive than mainland Italy though. I've found a fair amount of information on the island on Trip Advisor. http://www.tripadvisor.com

I know how horrible the drivign in sicily is and my friend's comment was "so you see it and then that's 1 day gone, what about the rest? why not go somewhere with art and culture like venice?" But that's not really the point. The point is to try and get a nonexpensive trip to see a volcano as close as you can without being a scientist/loony. Not exactly your average holiday plan, and no real need to take a week about doing it either really unless there is lots of stuff to do in nearby places.
It's a totally off-the-wall concept which is why I've not found anyone who can advise. But people travel the world for a few days for more random things than volcanos! It would be an unforgetable experience I think for people who have always been fascinated by them!

For a flight of less than a few hours Etna is probably your only bet in October , I hadn't heard that driving in Sicily was any worse than the rest of Italy, friends have just returned from the island and didn't say anything about it. I drive quite often in Italy so I'm pretty much used to the style of driving. I was hoping to combine seeing the island and volcano plus a couple of days relaxation. I don't live in the UK so can't be much help with flights etc. but hazard a guess that prices will be higher than other Mediterranean destinations.
Venice, Rome, Florence are of course great cities if culture is what's wanted and very good destinations for short breaks.. I hope you are able to find what you are looking for.

OK I've been looking around and these guys look good for an actual experience trip?
volcanotrek dot com

St Kitts Mt.Liamuiga Volcano Safari
http://www.stkittstourism.kn/EnjoyStKitts/Tours_Gregs_Safaris.asp
BA fly from the UK to St Kitts.

Thanks, that certainly looks nice! Though that's very inactive as oppose to active which is desired, and the flights just made my wallet flinch lol