As a kid growing up in the area, we always used to pack deli sandwiches and bottles of water and head to the Washington monument. We would get there well ahead of time (they used to have concerts nearby too) set up a spot to sit and eat/enjoy music and wait for the fireworks.
Its been 15 years at least since I have been down there, so I can't promise the music or ability to bring water, etc. Just about anywhere on the National Mall will be a great place to see from. The buildings aren't very tall, so you should have unobstructed views.
If I remember correctly, you would take the bus from the park to College Park Metro station (or drive there, only a couple miles) and take the green line to the red line and then the red line to the Metro Center exit. Its a couple minutes walk from there.
For those not familiar with the DC Metro system, its not like a standard subway with lots of stops. The stops are usually pretty far spread out.
DC in July is VERY hot and humid. It will be close to unbearable. Make sure you have comfy shoes, plenty of water and loose fitting breathable clothes.
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