Lucky you, 3 nights in Belfast! It is one of my favourite places. You would probably be best served posting on the Belfast section of the Northern Ireland forum for comprehensive local information. tripadvisor.ie/ShowForum-g186470-i491-Belfas…
In the meantime here's a few of my favourites to get you started.
In relation to food, you will be spoilt for choice in Belfast. There is a wide range of restaurants catering for all tastes and budgets and a lot of them are quite proud and pleased to showcase the wonderful local foodstuffs from the area . My favourites are Ginger Bistro http://www.gingerbistro.com/ and Mourne Seafood http://www.mourneseafood.com/page/14/belfast/ This is a comprehensive list to what's on offer foodwise in the city belfastcity.gov.uk/tourismguides/docs/Belfas…
My favourite area (slightly) away from the city centre is the Lisburn Road, Botanic and University area Lots of nice cafes, delis, shops with a nice atmosphere to amble around. http://thelisburnroad.com/
For music, it depends on what you are looking for. For traditional, along with a great pub - The John Hewitt must be on your list http://www.thejohnhewitt.com/
Again, dependant on what dates you are in the city, a night in the beautiful Grand Opera House could be on the cards. Have a look at the events here. I wouldnt mind the Chrismas Spectacular on 25th November
You will have the added advantage of the Christmas Market in front of City Hall as your visit is at end of November, as it started on 19th last year, so it will be well and truly up and running. If your visit concides with a weekend, a visit to the infamous St George's Market is a MUST. Full of atmosphere, music, local foodstuffs and arts & crafts. Only open on a Fri/Sat/Sun www.belfastcity.gov.uk/stgeorgesmarket/
In relation to the coast - you have probably answered your own question insofar you are "note really the organized tour types". Bear in mind though, that November season will be quieter with possibly less people on tours, and should the weather be bad, someone else has the hastle of driving. However, in saying that, if you do opt to drive, you will have the opportunity to drive to Torr Head. and stop/start as you want to, at your own pace. Torr Head is not a drive not for the fainthearted, but so worth it. Tour Busses and larger vehicles are not permitted on the road. If you drive it, you will see why!
This is a very good site with plenty of information belfastcity.gov.uk/tourismguides/index.asp
Edited: 19 August 2012, 18:07