Mykonos will be totally dead in February. Rhodes has a larger permanent population and some historical sites, but the islands are really summer/beach destinations, so I don't see rhe point. Thessaloniki is Greece's second city, so would be a more logical, but chilly, winter destination. The area around Nafplio is rich in historical sites, so would be my choice. You won't even have to get on a plane or ferry to reach it from Athens.

I have visited Thessaloniki in late March. It was ok some days but freezing the other days.

Ferry rides during winter storm can get quite exciting:
https://www.youtube.com/watch?v=QrzIgE7AOmc

Ferries do dock even during the inclement weather:
https://www.youtube.com/watch?v=S1xq_QtHmLE

Listen to Heimdall. Nafplio. Did you look at http://www.visitnafplio.com ??? Wonderful and Noncommercial website. It has a video of a Walk in Nafplio in early Feb., that shows how enjoyable & vibrant the Old Town is, even in Winter. It's where the savvy Athenians go to have an enjoyable weekend in Winter. They know.

RE "I've heard good things about Santorini" -- that means little unless the "things" came from someone who was there in Winter. If I had a dollar for every instance on these Forums of a person making iffy decisions on the basis of "I've heard..." I'd be a rich person today. Forum Regulars spend a LOT of time trying to untangle or roll back decisions that newcomers make on basis of unresearched hearsay. We aren't killjoys, we just want you to have a good time and not be led astray by wishful thinking.

Go back to all the responses that suggest Athens & Nafplio, it really does make the most sense in February.
Reasons Santorini is not the best choice in February:
The attractions are watching the sunset over the caldera, much less chance of there even being a sunset!
The brilliant white & blue of the buildings, not so vivid or appealing if it's cloudy & wet.
The changing colors of the buildings on the caldera as the sun goes down, see above.
Limited accommodation & taverna choice, many will be closed.
Lastly, you said you're budget conscious, it's one of the most expensive islands.

As I said above, Santorini pretty much closes down around November until springtime. Many workers return to Athens during the winter. I wouldn't suggest it in February.

cadd, re: the 5-hour 'fast' ferry, ours left Athens early in the morning and we arrived at Santorini around noon. It's a very nice boat, with assigned seats.

Cool, so I've booked 4 nights in Athens and I can book time in Nafplio also.

Is Nafplio a homebase of sorts where I should spend an additional 5 nights there and perhaps do daytrips (suggestions for February?) to surrounding areas? I'll plan on renting a car per the suggestions above.

Nafplio is an IDEAL base for day trips, perfect. You can easily spend 5+ days in the area and not run out of discoveries. I see that I gave the wrong link to the wonderful noncommercial website that gives terrific info not only about Old Town, but the entire surrounding area. Here's the link -- http://www.visitnafplio.com -- and here's the direct link to Hotel Agamemmon - http://www.nafplioagamemnon.gr/en/ ... one of the few hotels right on the sea front. And here's a wonderful photo Album of Nafplio, with a few of the local sights at the end ... it was taken in May http://www.flickr.com/photos/stanbr5...7632094108982/ -- but the landmarks and vistas just as lovely in winter.