James suggested sending a probe on ahead. There's a thought. What technology the probe is going to have will have variety, so that can be a fun problem solve. Can it photograph? Can it detect surveillance? Poisonous gases? Population? Radiation? Each variation would lead to a different place to send it, different conditions.
Probe or personal, the idea of scouting out Washington DC or NYC first seems problematic. While you could certainly get more information you need more quickly at a place like that, there would be greater risks as well. Not the place you would want to be walking around without identification or a good explanation for your appearance. High-value military targets, so radiation risk, ubiquitous surveillance. And if things had gone deeply wrong with American in 20 years or 100, DC might be the last place you'd want to see.
I am thinking that a place I would know my way around, but could still observe quite a distance while remaining hidden or less-noticeable myself would be good. If you could look down on a familiar city at night and see the lights were out, or no one on the highways, well, then you'd know that it's time to start covering some distance if you're a probe, or start looking for fresh water and a place the few remaining souls might show up. Communication towers maybe. Or more positively, if everything looks ducky down below, one could start acquiring info more boldly. Blue Hill might work for me, or Hooksett Pinnacle.
The point to go to the future would be either to get something cured/fixed, or to have some info to bring back to the present. Though if it were nice you might decide to stay, even though you'd be a stupid useless person yourself.