Ooof, Fort Meade was described
elsewhere (by a 10-year employee) as "a transit black hole with growing traffic and horrible parking." It's not exactly easy to get to from anywhere. There are
shuttle buses (http://meaderide.com/commuting/transit/commuting-from-maryland/ - broken link) from MARC's Penn and Camden lines and from the Metro Green Line, which apparently have expanded service since BRAC moved a lot more jobs to Ft. Meade. Do check first that your particular installation is on that shuttle route, since apparently not all of them go everywhere on base.
There also aren't many walkable, 24-hour neighborhoods in the eastern half of the DC metro area, or the southern half of Baltimore. If you're willing to tough it out some on the commute, though, you can find great neighborhoods just outside the respective cities' downtowns. In Baltimore, somewhere like Federal Hill (
most walkable neighborhood in town) is a 17 mile drive from Ft. Meade and that's almost all on relatively uncongested freeways. Downtown Baltimore itself, or the new Harbor East area, are also options. Plus, Baltimore apparently offers
DoD-specific relocation kits. Note that the MARC Penn Line to Odenton leaves Baltimore from Penn Station, which is about two miles north of downtown, while the MARC Camden Line to Savage leaves from south of downtown next to Camden Yards (near Federal Hill, or the tiny neighborhood of Ridgely's Delight). The harborfront trail in Baltimore is beautiful, but gets tourist-infested in the summer; from Federal Hill there's also a trail headed inland to Gwynns Falls Park.
In DC, I'd consider the neighborhoods behind Union Station -- to the west, Mount Vernon Triangle and NoMa, and to the east the H Street area of Capitol Hill. It's the only location in town that would give you the option of either taking MARC (both Penn or Camden lines) or driving (24 miles, but more local streets and much more traffic). They're all "up and coming" neighborhoods, unlike the very established Federal Hill, but just in the past year or two have really started to blossom with new retail. MVT and NoMa are all new high-rises, whereas the Hill is all historic rowhouses. Technically, the Green Line is an option with the new Greenbelt-Ft. Meade shuttle, but I'd imagine that you're looking at 50+ minutes from Columbia Heights or U Street (the most walkable areas along the Green Line) to Ft. Meade. As for running, Union Station is the start of the Metropolitan Branch Trail and just north of the Capitol, where you can get to the (tourist-thronged, but soft-surfaced) Mall and the Potomac; at the Hill's eastern edge, the Anacostia River Trail now forms a complete loop.
Sadly, people like you aren't in charge of DoD location decisions -- otherwise, they wouldn't move tens of thousands of jobs from the region's core to exurban nightmares like Fort Belvoir and Fort Meade. The result is unhappy employees with long commutes, plus much worse congestion, pollution, and sprawl for everyone. There are secure military sites much closer in, but I guess they'd rather reserve those for -- well, I don't know what goes on there (and I think they prefer it that way).