I run a Machine Learning consulting business. Been fully remote without a 'home base' for about a year. Really loving it so far and plan on continuing for the foreseeable future!
My advice would be to spend at least a month in each place - it's also a discontinuity point in accommodation pricing. AirBnB snaps into monthly discounts and it's the minimum period for short term rental. Definitely just google "city name short term rental" and look at the local sites - you can find some amazing apartments for a month at a time.
I'm traveling with my girlfriend who works in online marketing. I believe it makes it a lot easier but we've been together the entire time so I can't make a fair comparison. I can see how it might get lonely but I really enjoy hanging out with the girlfriend and go to meetups while traveling so haven't felt lonely at all...