I haven't biked in DC for more than a decade, but when my wife and I visited with our bikes, here's the ride we took.
http://nyrides.freehosting.net/dc.htm . This is a link to a page on my website. Conveniently, we stayed at a hotel in Greenbelt and took the train into town, which saved a lot of hassles, as DC is known for horrible traffic and very scarce parking. I'm not sure where Greenbelt Park is, but it can't be far from where we spent the night.
I'd assume Alaska is a bit like a place I used to do business in Canada, called Yellowknife. If so, DC is not much worse than that. Everywhere you go, there are good sections and bad. When we visited DC, there were definitely some characters that made us feel uncomfortable on some of the streets, but being from New York, we are used to that. Others here can probably tell you which neighborhoods to avoid, but I think if you stay in the typical tourist section, you'll be OK. Remember that the guide sheet on my website is quite old, so be sure to confirm it all with other readers.
Please report back after your trip!