A lot of this info could be dated so good to double check.
It's hard to make a "not to miss" list as people prefer such different things but here are some comments:

Liwonde NP - this park is easy to get to and has various types of lodging

Nyika NP - a very special park but a bit more difficult to get to and only one lodge (Chelinda). It's very beautiful but on the spendy side.
Previously they have had self-catering cottages but not sure about now.

Vwaza NP - were there in 2003 so may have changed a lot. We stayed in thatched huts on cement foundations and the hippos wandered around us at night.

Majete NP has had good reviews but we haven't been. We would be keen to try it next time.

Mulanje - good for hiking. The area around is full of tea plantations. Various types of accommodation but not far from Blantyre so doable for day visits if staying there.

Zomba plateau - nice place for walks. Zomba town is nice as well.

Dedza - we've driven through and stopped for lunch - pretty place.

Livingstonia (northern Malawia, not at the lake). We lived here for 2 years so I am biased! A bit quaint perhaps but beautiful location.
Previously could be quite time-consuming to get to without private transport but they have started to pave the "back road" up so this could be changing.

The Lake - Likoma is lovely. The ferry doesn't go very often so a bit time-consuming. Flights can be expensive.
We've been to Chinteche (reasonably quiet), Nkhata Bay (busy) and Nkhotakota (only 1 night and not sad to leave)

Mua - an interesting place to visit - the Museum is good and if you get to meet the Fathers it can be fun.

The "difficult to get to" is based on our own travels which is mostly by public transport. We have hired a car a few times.
As with many countries, a healthy budget will make things easier and faster (hired cars, air travel).

Happy to answer more questions.