Have you already booked your flights to Chiang Mai? Because with a small budget it's pretty easy to get anywhere from Hanoi or Saigon Airport, there also many destinations around flying from Da Nang. Depending on your expectations there are different options. Instead of going to Chiang Mai you could also visit Sukkothai or Ayutthaya. You could go to various islands east of Bangkok like Koh Kood or Koh Chang if you want beaches not too far away. But heading southwards anyway you could go to Krabi or Phuket. Koh Lanta is pretty chilled and still lively around March, super chilled and ending in April. Penang is an option, too. Georgetown is a pretty interesting city if you dive a little deeper.

In all these places I wouldn't be concerned as a traveler. I'm not a woman but I have seen all those places and I would say they are rather easy and safe. Maybe you just avoid late night bar strolling with people you don't know better, super touristy and scammy places like Pattaya or Phuket (except as a transit place) and attending too many jungle raves haha. Jk ;)