If your friends don't mind a 10-15 minute walk, how about going to Penn Quarter? There are many restaurants there, even Carmine's (from NY) which is a great family place. There is also decent brunch a the Hotel Monaco as well as Jaleo and the District Chop House.

If you don't want to get a suite, one possibility is for you to get a larger room that fits an extra rollaway bed. This way, you can create a sleeping area for your child and follow a similar ritual as at home. Nicer hotels have high quality extra beds from our experience. I agree with other posts that sleeping at a similar time as your child helps. Last, if you are planning to stay at hotels more often going forward, you may want to create a special routine with your child and explain beforehand. We have been traveling all over the world with our child since she was a baby and she now at age 5 has a routine for both on the plane and at hotels.