There are two Sport & Health gyms in Crystal City. S&H Crystal Gateway is on the north end, at 1235 S. Clark St. (It’s possible that this location will be converted into a climbing gym early next year.) S&H Crystal Park is at 23rd & Crystal Drive, which is closer to 2800 Crystal Drive.
There is also an LA Fitness gym at National Gateway, Rte. 1 and S. Glebe Rd. I don’t know if they have shower-only memberships but you can check. Be careful before signing any contracts at either gym. They like to lock people into long-term memberships and they aren’t always responsive when people try to cancel. Trial memberships are also tricky, especially if they require your credit card info before you get the trial membership. They will try to roll you over into a regular paid membership.
2800 Crystal Drive is just about at the midpoint between S&H Crystal Park and LA Fitness.
I don’t know which buildings have bike cages. I’ve seen some in other buildings. I added them to the RackSpotter map but I haven’t checked every parking garage in the neighborhood.
During the workday, if you don’t want to get your bike out again at lunchtime, you can use the new Metroway bus rapid transit route that runs through Crystal City, Potomac Yard and (eventually) Pentagon City. There are also Capital Bikeshare stations throughout that area. Those bikes can let you get to more lunch places without having to get your personal bike from a bike room.