This is a matter of travel style, and I fear you two may not have the same style. It's also the way students traveled in the 1960's. I think it's less common today. It will take time away from sightseeing to do the bookings, and you may have to pay a walk-up rate or go farther to find a place with room, before you can even scope it out from the exterior. I know people believe that Hotels dot com has cheaper places at the last minute, but are you staying in real hotels?
I would not do this, but I'm 71, and there's no reason another person should do it my-way.
I have never had the experience of being sorry I went to particular city, but my wife and I both dislike frequent hotel changes, so we book 3-night minimums, and take train daytrips if the city turns out not to have quite enough to see. Sometimes packing, unpacking, copying passport data, and getting (?) cash to pay a tax-evading B&B can take more time than you think. Opinion.
Some of the sights in Portugal, like Roman ruins, Templar castles, monasteries, and so on, are quite spread out. I am sure your boyfriend will be horrified by my post elsewhere
https://community.ricksteves.com/travel-forum/portugal/7-nights-in-lisbon
about using a BUS company TOUR to hit three or four high points in a full day out of Lisbon!
I am sure your question has come up here before, at least in the general case. See Search box top center.
Edit: If you go to the TI to see their list of low-cost lodgings, you may have a low-cost teenager behind the desk, who has never met a single owner who posts their room at the TI. And if the TI is closed today?