Yes and no - we are budgeted flying hours, but we don't get to choose what we do with them.
For those unfamiliar, USAF crews have semiannual training requirements they must complete in order to maintain status. For each requirement, there will be some number of iterations or hours, such as six Visual Laydown bomb deliveries, ten ILS approaches, two air refuelings, etc. Scorable events may also have accuracy requirements, such as having a CEP inside 200 feet for all the VLD bomb runs attempted. These are set by aircraft type/mission, and will be significantly different for an F-15 versus a C-130. Crewmembers are held accountable if they don't complete all their events each half within parameters. The scheduling and training office would track all that stuff, and make sure you got enough opportunities for low-levels, range time, tankers, etc., to fill all the squares. So, if they said you're going to Melrose range to drop bombs from 1000-1030 today, you didn't get to say, "Naw, we'd rather fly a low-level to the RBS range in Kansas."
Def don't get to fly off someplace for lunch - at least not with real jets. We did that in pilot training because they are fuel limited and have no classified stuff on them.
The Navy guys I know get to do some of that. The AF has too many rules.
We were able to fly places for the weekend in USAF, ANG, and USN jets, and even for turnround missions (i.e., for lunch) as long as we got training events done each way and the place we went was appropriately secure.
Thus, we could fly an F-111 from Cannon AFB up to Mountain Home AFB, refuel, and come home, as long as we got training each way -- say, a low-level into Saylor Creek Range for a few bombing runs on the way up, and a low-level back to Melrose Range for a few more bombs on the way home. 'Course, lunch at the Mountain Home flight line cafeteria wasn't much to write home about, but it got you out of the office all day.
Another time, we took an F-111 for the weekend seafood tour -- launch from Cannon AFB NM with an RBS run somewhere in Kansas on our way to Eglin AFB FL (where they had a few F-111's so they could fix us if we broke) for shrimp night at the O'Club there, then on Saturday via a low-level in the Carolinas up to Pease AFB NH (an FB-111 base) for Lobster Night, then home on Sunday via another RBS range with about 140 lobsters in the weapons bay for the rest of the squadron to have a lobster boil Sunday night.
Likewise, in the ANG, we used to launch out of Standiford Field in Louisville about 7 pm on Friday night in an RF-4, fly a low-level up to Wright-Patterson AFB OH, land, park the jet, have a few beers and dinner in the Rathskeller (basement of the O'Club), spend the night in the BOQ, and then fly another low-level home next morning to arrive as the ANGB opened at 9 am on Saturday so they could turn the jet for a 10 am flight by someone else. Nice way to get two days' pay for 8 hours work and a night in Dayton while filling training squares. Also improved the utilization rate on the jets as that way we got three training hops out of the jet on Saturday instead of just two.
But maybe that's all changed in the last 20 years...