Working backwards:
There is a gym in Forest Hill, it opened two years ago and seems well equipped. There will be a gym in the swimming pool when it opens in September.

Crime is the same as most similar areas of London. Not noticeably different from East Dulwich.

There are a number of relatively new cafes in Forest Hill including From the Forest, St Davids, The Brothers, The Teapot, Black Hummingbird, Horniman Museum cafe, Horniman Triangle cafe, and the swimming pool will have a cafe. Honor Oak also has cafes, particularly Hop Scotch.

Forest Hill has quite a large number of pubs which cater for all types. You may particularly enjoy The Honor Oak, Dartmouth Arms, The Hob, and All Inn One, and Try as they are probably the most popular with young couples.

Don't forget the great views, the museum, the parks and woodland, and a number of very good restaurants (Babur, Le Querce, Dartmouth Arms), outstanding schools, and good value houses (compared to East Dulwich or many other parts of London).