Housing in DC is very expensive. I had a large bedroom in a shabby shared house for $600, and a nice one bedroom in an older building for $1500. Both of those would be considered great deals, especially given they were in central locations. Less expensive rents can be found on the edges of gentrification, but those edges are getting pushed pretty darn far. The good thing is that sharing a house is considered a perfectly reasonable thing for an adult. It won’t raise any eyebrows in dating, and it’s not hard to find a more mature roomate. If you are lucky, you can find a roommate who travels often for work, and you may end up with the place to yourself more often than not.
You are right that entertainment is easy, especially if you consider policy talks and book signings to be “entertainment.” You could stay busy every day of the week and not pay a cent-- and probably keep yourself relatively well fed with complimentary cheese and wine. But DC does have a big happy hour/foodie culture, and that can get pricey quickly if you have an active social life and try to do it all.
Despite the costs, I think it’s a good place to be starting fresh as an adult (I don’t know how old you are, but I assume you aren’t fresh out of college.) The economy is good, and there are a lot of unusual opportunities. I know dozens of people (myself included) who came here without jobs and knowing nobody, and have managed to make good lives and real careers for themselves pretty quickly- there is just a lot of opportunity. And because it’s a place with lots of transplants, lots of career-changers, and lots of single folks, it’s easy to make friends even as an adult.