Catania hotel recommendation in center for 6:35am flight departure

Joann,
On our first visit to Catania in 2014 we spent our last night at Liberty Hotel in the city center.
We had an early flight to Rome and it was only a 15 min. taxi ride to the airport. liberty hotel.it.
It was fine for one night.

Edited to add: To the best of my recollection we got to the airport a couple hours before our flight.

When we were returning to Sicily in 2020 (canceled due to lockdown) we had planned to stay at B & B Palazzo Bruca Catania in the city center. This accommodation was highly recommended by another forum contributor. We would book again if or when we return.
http://www.brucaroomhotelcatania.it/en/

I'm one of those people that likes to get to the airport early.
My flight from Catania was mid afternoon, not morning, but I couldn't even drop off my bag until much closer to flight time, I don't recall exactly how long before.
I suggest you get info from the airline about when they want you there. Also, the airport is compact so you will not need much time to find your way once you arrive.

I also have a 6:35am departure from Catania, for a trip that may end up cancelled anyway. It seems that as of late, 2 hours before is the bare minimum for flight departure. I know I wouldn't be able to sleep and since we'd have to leave at 4am or earlier, at some point, does it just make sense to go to the airport the night before?

When we were there, we had a taxi pickup at around 3:30 AM, no issues. Hotel took care of arranging. Dont remember the name of the hotel, but it was pretty routine for a hotel to handle this. Just ask them when you arrive. Some airports won't stay open and let you stay there 24 hrs.

In Sicily it may be closer to two hours if you have all your covid documents and can easily check bags. I took a cab that was the fastest cab ride of my life. The driver thought he was a formula 1 driver but drove a piece-of-shit car. Still made tires squeal on some corners, went 4 abreast down the 3 lane road until someone backed off, cut through a parking lot at 70 kph to avoid a slowing driver at a round about. Got to the airport and realized I was holding my breath the whole way. 10 minutes tops.

We arrived at the airport 3hours early, but had to return a rental car. It is a compact airport as someone else said. Can’t help with a hotel in town since we stayed at a nearby military facility a few miles south of the airport. There are a couple hotels very near the airport that might be worth checking out. At least the city and airport are very near each other.