What to do in Bali for few hours overnight?

Landing on a Sunday afternoon 3:45pm - given what I have read on this thread, I would not expect to get out of airport to a taxi until 6+pm.
I have a hotel in Legian and need to be back to the airport ~7:30am - I expect minimum 45min travel time.

What, other than a hot shower and attempt to sleep to get on schedule, should I even consider trying to do?

1) I don't think we've ever spent more than 45 minutes elapsed time from the time we exited the aircraft until we exited the terminal, having purchased our 30-day visa on arrival, cleared customs and immigration, and claimed our luggage in that time. Just don't dawdle between the plan and the VOA window.

2) If your hotel is only a place to shower and catch some sleep before departure, why are you going way up to Legian? Here's a great hotel and spa, huge rooms and beautiful pool, quiet setting, 5-10 minutes from the airport:

Green Garden Hotel Bali beach resort - Bali Hotel Kuta - Bali Cheap Hotel

You pay for a taxi to the hotel (again, it's very close), and they shuttle you in the morning, included in your room rate. While it says "beach resort," it's actually 100m off the beach, on a very quiet back street. They have a restaurant, but I wouldn't recommend it for dinner. There are some great places within a five-minute walk. I'd ask in advance for a room above ground level. If you check the Asian hotel reservation sites, you can get a room well below their advertised rate, or just email them and ask what their best price is if you book directly. They're very well organized, and will reply quickly.

There ... your Bali overnight is much easier now.

traveling time from kuta to airport is only 10 minutes the most in the morning. expect long delay if you fly with merpati or garuda domestically

Have dinner, find a girl or boy, get a massage.
Kuta business area is the real bottleneck. You should get to hotel far before 6pm, but depends on what scheme Immigration is trying out this time. Sometimes, they really screw things up, then everyone complains, so they change the way they do things.
By allocating 45 minutes to get back to the airport that early in the morning, you should be able to sustain two flat tires and an auto accident. Of course, the airport is sooo charming that you may wish to allocate extra time for contemplating its beauty.

High desert - Thank you for that great info, but I did not interpret ~2km as being "far" from the airport and I was able to get a very nice (?) hotel "The Stones" for points; As it is associated with the Marriott chain, I have "status".

It is great to hear that Immigration and street-level travel MAY not be as bad as originally estimated!

Kilili - I calculated that I could potentially walk the distance (and have the time in the morning heat and humidity) with all my gear should the 3rd & 4th tire blow... So, the Bali airport is as "nice" as the Jakarta terminal system?
After 20+ hrs of travel a massage sounds like a good idea! Is it pretty evident which are the "standard" deep tissue massage places? (I'm not looking for any "additional services")

No idea who the domestic connection will be with - we are flying DPS to Bima to catch the boat.

Only Merpati & Wings fly to Bima. You know the time, just need to check the schedules via the web. The domestic terminal is not nearly as nice as the international one.

Your hotel will easily be able to arrange a "normal" massage. If you're walking about, pass by girls on the street and shops down the alleys, and don't ask a cab driver.
There are places everywhere, but many girls are not that skilled. The more upstream the place, the better chance you have of getting someone with skill.

Don't recall the name, but my favorite is across the street from the bombing memorial on Legion in Kuta. Its 2-story, and the side window has a sheet of water running down it.