Silver Spring is a big area, but if you are in the part of Silver Spring inside or near the Beltway, the obvious answers are Rock Creek Park and Sligo Creek Park. In Rock Creek, the hotspots during migration are the maintenance yard (parking lot, open area behind the maintenance building - just follow the other birders) and the area around the stables. There are other good places, especially along the creek itself. I can't speak to specific places in Sligo Creek Park. 

These are probably close enough to you to be good pre-work spots, depending on where you work. 

In other seasons, birds are dispersed throughout the park. We hike (Valley Trail, Western Ridge Trail) and they are not very birdy. Tons of robins, occasional woodpeckers, peewees...the deer browse is massive so there is no understory at all in most places. Plus tons of hikers, runners, dog walkers. We see Mallards, Black Ducks, Wood Ducks, and Kingfishers in/near the creek. Baltimore Orioles in/around the sycamores. Yellow-billed Cuckoos and once in a while, a Black-billed Cuckoo. 

A good website generally for natural areas in the vicinity: http://www.thenaturalcapital.com/

The Wild Bird Center, MOS chapters, and the Smithsonian all offer local bird walks (the Smithsonian walks are part of the Smithsonian Resident Associates program and often are broader in focus than just birding; they are also somewhat pricey but led by experts who make the experience and cost worthwhile). 

Ellen Paul
Bethesda MD