web sites lodging

Booking .com
And you can trust the reviews there as they can only be left by folks who have actually stayed at the property

You can narrow your search by using the filters-location, budget, AC, elevator, bkft, wifyoj can also filter reviews for things like good WiFi, view, noise
You can safely book there or go to the hotel’s own website
Your choice

For vrbo-use the vrbo website
For Airbnb-same

I start with Booking.com. I often will filter the search by low price to high price and then look for properties with the highest customer ratings in that given price range. Never been disappointed.

Another method is to go to Google Maps and pull up the city and neighborhood I want to stay in. Then I'll go to the top and click on "Hotels". Up pops a bunch of icons with prices on them. You can go from one to the other and click on their direct web sites. You can also read customer ratings, etc. Again, I've never been disappointed.

Rome is one of those cities with hundreds and hundreds of places to stay. There, I will expand the map on Google Maps to the neighborhood I like. I like the Pantheon area. I also like the San Pietro/Ottaviano underground station neighborhood which is close to the Vatican Museum and within eyesight of the Vatican. You can get there from Termini on the Underground quick and cheap vs. having to take a taxi.

Another fan of Booking.com. I’ve been using them for several years and appreciate their options, message options, and having all of my reservations available in one website.

Yep, another booking.com fan.

Call me an old fashioned luddite, but we use various sites to do research, and then book directly with the hotel. We have never been unable to book directly. In the event of a snag of some sort, it's much easier to resolve when dealing directly with the hotel itself. Just my outlook. Others may differ, and that's ok -- to each his own.

Hotel.com has always worked well for us.

I use the mentioned websites for research, but then go directly to the hotel site to book. Non-chain hotels often offer 10-15% off or free breakfast to book directly with them. It also makes it easier to ask for the location of the room (high floor, away from main street, etc.). And, there should be no surprises that the type of room you booked in terms of number of beds is no longer available.