Chris-
I've not been back since 1970 but believe that you will still likely find the Bayswater and Lancaster Gate tube stops within easy reach of your gunshop destinations and all of the tourist stuff. Back then Bayswater had more than a few Indian restaurants and a smattering of small pensions and hotels. As you head further east along the northside of the park toward Lancaster Gate and Edgeware Road tube stops, things became a bit more upscale, but nothing like the east, south and west side of the park-Mayfair, Knightsbridge, Kensington, etc.
Another alternative but still very accessible location is Hampstead at Hampstead Heath-your wife will adore you for booking her a place nearby, and you can take the "little monster" to the heath to practice his dribbling. Same area-another tube stop-St. John's Wood. Delightful area and shops.
Suggest you do some word searches for pensions and B&B's in these areas if they interest you. Since you are going in off season, rates may not be as dear as now.
skatr2