I am not arrogant enough to pretend I have all the answers but I have maintained for years that there are some really simple things they could do to improve F1.
One is to force them to use as much fuel as possible -> set weight limits so that the cars should leave the pits heavy with fuel but at the end of the race should be running on fumes - they have controlled fuel usage limits so it would be easy to calculate these weights. Yes of course there would have to be tolerances for safety car periods etc. but this is still possible and would avoid fuel saving issues during the race.
The other easy one (even under current regs) is to force a bigger differential between the three tyre types made available and make the tyres less reliable i.e. genuinely allow strategic choice of how many pit stops will be fastest for your car; smooth driving and a good car set-up is rewarded by fewer sets of tyres being required to last the race, or create some jeopardy by risking that some hard charging may need an additional pit stop or seeing if the tyres may maintain grip to the end of the race.
The fuel one is touchy, in a world of 'green' aesthetics, having an F1 car burn as little as possible and win makes sense. I do miss in race refueling, it was possible to push hard and then dive in to top up. I do understand that refueling is a disaster waiting to happen, and understand not taking that risk.
I'd be okay with taking pit stops out of the race entirely, with drivers staying on the same set of tires all race (designed to do so). Without the possibility of over or under cuts, the drivers know where they stand and won't take a 'wait and see' approach.
Also, if Pirelli was allowed to create a tire that was designed to last AND increase grip (which seems entirely plausible to me), then we can remove aero from the cars without forcing them to slow down.