I think you'll be somewhat surprised by Anchorage's high cost of accomodations during the summer high season. The Hilton, Sheraton and Regal Alaskan all command prices upwards of $200 a night. Less expensive alternatives are B & B's, of which there are plenty, or motels, many of which are a little less than well kept.
As many flights arrive in ANC at night, the tourism industry is set up for the "late" arrivals and the airport car rental and hotel shuttle services are offered well past midnight.
July 04 will be just a little after summer solstice, meaning that daylight will extend well into the wee hours of the morning. July 04 fireworks will be later than you are used to.
As Anchorage is a relatively small city, the airport is but a few minutes away from any given hotel in the downtown area, and usually no more than a half hour from most suburban B & B's.

Restaurants on the recommended list include:

• Simon and seafort's on L St.
• Jen's Restaurant on 36th Ave.
• Crow's Nest atop the Captain Cook Hotel on 5th Ave.
  

Hope this is of use.