Hootananny is a wonderful venue for music and pub food. Check out the Victorian Market.
If you want some lovely jewelry for yourself or someone else, I love Hazel Passmore's designs. Her website isn't up yet. You can find her studio/showroom at 25 Inglis Street, Inverness, Scotland IV1 1HN, United Kingdom
+44 1463 715231. It is right across from the Railway Station. The Mustard Seed is a good restaurant. One of the great used bookshops of all times, Leakey's Books is in Inverness.
For short walks there are the Ness Islands.
When you go to Culloden, you'll find that the public bus is quite easy. You can also walk over to Clava Cairns and back. I didn't look to see if there is a public bus to either Fort George or Cawdor Castle, but it might be work checking them out. I don't think you'll need a full day at Culloden, a good half day is probable though with your interest. A taxi to these locations is likely not outrageous. But there is a great TI in town. It's not at the RR station, but is over by the bridge. It looks like you'll go right past the TI on your way to your B&B.
You might also want to see what's happening at Eden Court.
I've never done any walking tours. I'll be interested to know if you hear of any or try any out.
There is a football club, Inverness Caledonian Thistle and it would be fun to go to a match if your travel schedule matched theirs. I can't figure out the schedule, but I'm sure M. C. or UncleGus can help with questions. I've driven past the stadium in September when a match has been on. They compete in the Scottish Premiership League.