Gravelly Point is a wonderful place to view the fireworks. And, there is the "relatively" close option of the airport terminal if the weather gets bad. The other suggestion of Long Bridge Park is good, too.

Also, watching from Columbia Island (which seems like it is on the Virginia side of the river but is actually in DC) was a long-time tradition of my "crew" during high school and college days. Back then, before bin Laden won and our feckless parents (and now feckless us) weren't in control with so many "securitay" restrictions, one could make a truly wonderful day-long picnic of it - complete with adult beverages and even grills. But it is still a spectacular vantage point with the entire city as your backdrop (similar to watching fireworks from Jersey City with Manhattan behind). If you have a car, parking is plentiful and free at the Pentagon North Parking lot and it is an easy walk across the bridge to the LBJ Grove and then across GW Parkway to the water's edge. For some years the Park Service has put up webbed construction fencing to keep cars from parking on the grass which may cause a little bit of an issue getting to the grass areas along the waters edge.

For the W hotel rooftop bar - VUE - they are currently taking reservations VUE Rooftop - Washington, DC - Washington, DC | Tock (exploretock.com) includes buffet and open bar for $200pp which sounds like it is in your budget.

Another great location would be on the DC Southwest waterfront - I used to watch from my family boat and the yachts I crewed on. Now that it is all renovated you can probably watch from the rooftops of some of the hotels and condos there. Watching from the Salamander (formerly the Mandarin Oriental) would be another prime viewing location. Happenings at Salamander Washington DC | Dining at The Lounge (salamanderdc.com)

Lots of options - just gotta be keep looking. Good Luck!