Presuming you’re flying into Havana…
– 3 nights in Havana. Go to Tropicana – it’s expensive but awesome. Check out Playa del Este, see the Malecon, etc.
– Rent a car, if you can. It really gets you out of the way and off the beaten track; plus driving between places is fascinating of itself.
– Vinales, Pinar Del Rio, Cayo Jutia. Beautiful part of Cuba, lovely to explore, and easy driving.
– You may find it worth heading further to Maria La Gorda, which is an “end of the road” resort on the western end of the island. It was cool when I went, but that was a few years back.
– Varadero may be worth a visit, or not. It’s a slightly faded resort peninsula, but kinda fun to see.
– Trinidad
– Sancti Spiritus is well worth checking out.
– Santa Clara, personally I didn’t rate, but it has a lot of historical stuff from Che.
– and think about spending your last few days at Cayo Santa Maria or similar, in an all-inclusive 5* (for Cuba) hotel. After beans, rice and chicken/ pork/ fish for 3 weeks, you may appreciate it!
I haven’t been east, but I’ve heard Santiago is fantastic, although a long drive.
There are some cool places up in the hills from before the revolution, IIRC one’s San Miguel de Los Banos, which used to be a spa town but now is abandoned. It’s very safe as a country (apart from the usual bar bill/ currency exchange scams), so explore!