You won't actually be crossing the highway if you stay at the Hilton. You'll be walking across a bridge. It might feel cutoff from the Wharf, but it's a 10-15 min walk. Additionally, the area the Hilton is in is closer to the Mall, in case you want to walk around the monuments or visit any of the musuems (most are free - I recommend the Hirshhorn as a must-see. Artechouse isn't part of the Smithsonian and you have to pay, but they sometimes have cool stuff).

Parking, unfortunately, is probably going to be pricey. The only downside of staying at the Hilton is that there are a lack of restraunts in that area. But if you are hanging out around the Wharf, there are a ton of options. If your hotel allows you to leave with your car and come back without paying again, you could drive to Union Market, H Street, or 14th/U Street and probably be able to find street parking. These areas all have a plethora of good food/nightlife options (well, Union Market doesn't have much nightlife).