Fewer places, and it's not close on that budget. Every move costs you a travel day, a booking fee, an arrival afternoon spent finding the supermarket, and usually a night of bad sleep. Four cities in fourteen nights is realistically eight usable days out of fourteen.
The solo angle makes it stronger, not weaker. Alone, the good part of a trip is the third day in a place — when the café guy recognises you, you know which tram goes where, and you've got a loose plan for the evening. You never get to day three if you're moving every three nights.
Two bases, one week each, day trips from both. That's what I'd book.