I would try South Queensferry. I can see it over the water from my window. Very quaint old town, think cobbled streets lined with hotels, bars and restaurants.
Here's a lovely hotel, but there are more:
www.oroccopier.co.uk/
Too many restaurants to list here.
You can do a lovely boat tour on the Forth. They do sailings during the day and disco/Jazz cruises at night.(Maid of the Forth or Forth Belle).
You can get a train in to the heart of Edinburgh, which only takes 10 minutes. For the best and poshest cocktails in town, try The Dome :
www.thedomeedinburgh.com/
You can get a 3 course lunch at Cafe Jules, for just £9.90
www.chezjulesbistro.com/menu
So much to do in Edinburgh, it's crazy.
If you had a car you could also go up north - St. Andrews etc.
We did Belfast recently, and that was really nice.