In my experience, if you can find a place that doesn't show a price on aggregators like Google Hotels or Booking.com, because its booking system is primitive, it's likely that it'll be underpriced. I once found a pension/hotel in Barcelona that cost way less than it should have for our dates, because a big conference was in town driving up prices for the "real" hotels with proper revenue management.
Now, where to find places that don't show up (or rather, don't display a price) on the aggregators? That one in Barcelona I found on Wikivoyage, so my advice is go to Wikivoyage and look at the places they suggest. For
Rome it says "Individual listings can be found in Rome's district articles", e.g.
Modern Center so give the links they provide there a try. Links might have died which probably indicates the place is no longer operating, but you can also try googling for their in case they changed their website.
If the booking link on hotel website leads to Booking.com or something then there's no point in even inputting your dates because you already tried Booking.com! But if it leads to a calendar that looks like it was coded up in 2004 you might be onto something.