I live in Chiang Mai and thoroughly recommend visiting - beautiful temples, great for culture and cooking lessons and under normal circumstances fantastic for getting some special clothes made, although right now many of the tailors are closed. It has lovely hiking trails if you are into that. It is also easy to get to Pai, Chiang Rai and the Golden Triangle from here - also all recommended. I also love going out to Huay Tueng Tao lake for a weekend lunch, and Doi Inthanon when we have a bit more time.
Sukhothai is a few hours drive south of here, it is worth stopping off for a day or two. Sukhothai kingdom was the first capital of Siam. Alternatively if you are pushed for time, Ayuttaya can be reached from Bangkok - many taxi drivers will offer to do a day trip.
We just got back from the Anantara Golden Triangle, I have held off doing elephant activities despite having been here 3 years because I didn't want to support an unethical one accidentally. The elephants had a lot of freedom and seemed very happy. No riding allowed. It is expensive though
For islands, I love Koh Samui. There are some fantastic places to eat and it is a fun island to explore. The Fisherman's Village is the best area to stay. You can easily get across to Koh Phangan too. Angthong National Marine park is great for snorkelling day trips, my friends even saw whales there a few months ago. For scuba diving Koh Tao is wonderful and if you want to get your padi certification you can do a course there.
Also as others have said, don't write off Bangkok straight away, it is a fun place to visit for a few days
Thailand is hopefully starting to open to tourists next month, although you can actually get in on tourist visas at the moment but you still have to to hotel quarantine.
If you are a confident and capable driver Thailand is actually quite easy to drive around. I wouldn't recommend it in Bangkok, but we regularly drive cars and mopeds around all the other places I have mentioned. It means you can explore places off the beaten track.
Regarding weather, January is a lovely time to be here, sunny but not too hot. But I see your plans have now changed to March. The weather will be good then but In the North it will be well into smoky season, when farmers and hill tribes burn crops and woodland causing extremely bad air pollution. The AQI gets extremely high to dangerous levels and locals stay inside where possible with air purifiers on full 24/7. If you are keen to visit/explore the north it may be better to wait a couple of months. It usually begins to improve after the Songkran festival (about the 14th April) but it depends when the rain starts.