I did a solo trip in the middle of February a few years back to Orlando. Found a decent hotel right near Grand Cypress for dirt cheap, was able to play 36 there one day and 36 out at Orange County National on another day. It’s not the best in terms of stimulating architecture, but at the time it was pretty convenient and didn’t break the bank. Now, you could probably day-trip down to Streamsong as well from Orlando and squeeze in 36 there as well.
Just a little warning about PHX/Scottsdale as well as Florida in general in March, prices may be a little higher all the way around as compared to February because spring training for baseball will be going on in those places.
Having grown up in South Carolina, you will likely get some decent weather in either of the Carolinas in March, especially if you’re going later in the month. You could easily do 36 for 3-4 days in a row in the Pinehurst area and not play any of the courses at the Pinehurst resort, there are that many courses in a small area down there. If you do go there, make sure you play Dormie Club while it’s still public, it will be going private soon.