Hi,
We go to the gym at Clube naval - if you are cost conscious it is great, although less fancy than the Physico, or the one at SuperMares. You get access to the pool which is very nice - we mostly use the pool, in fact.
There are also running and biking groups active.
I am a non-meat eater so the seafood here makes that pretty easy. But the Bel Piatto on Julius Nyerere has nice pasta, soups and and salads including vegetarian. And all the pizza places have at least one or two veggie choices, try El Greco on Julius Nyerere.
Have you tried Matapa yet? It's a traditional mozambican dish, normally served with prawn or crab, but you can get it without, and it's really great!
Good luck!
Mari