Would appreciate any specific neighborhoods that would be good for a 15-25 min bike commute to work downtown. Looking for cheapish sublet for a few months and good bike lanes. Thanks!
mozar's neighborhood recommendations are pretty spot on. I'd add in Edgewood as well. Downtown now stretches pretty much contiguously from Foggy Bottom to Union Station, and if you're working on the east end towards Union Station then the neighborhoods s/he mentioned will be particularly easy to bike commute from using the Metropolitan Branch Trail. Generally, the further east you go, the cheaper the rent, but it's also possible to find reasonable rents in neighborhoods west of Rock Creek Park, which might be more appealing if you work closer to Foggy Bottom/Dupont/Golden Triangle. As mentioned, you can find the best deals if you are committed to biking everywhere, and don't mind being over a mile from a Metro station. There are even decent deals to be found in Glover Park, Van Ness, and even Cleveland Park if you look further away from the Metro stop, and those areas are generally safer and quieter than the more eastern neighborhoods.
As for the OP's question about gyms: find out if your work building has one since many do. If not, cheaper options include Planet Fitness and (I'm told) Gold's. I'm not mustachian with my grocery purchases (a mix of TJ's, Harris Teeter, and Whole Foods), but I think there's an Aldi in an autocentric part of Northeast DC.