I'm sorry, but only you can know what too fancy/too basic means. If you have a budget number, that would be a better place to start.

You might want to peruse the website booking.com. You can set parameters of property type (B&B, hotel), rate, location, amenities you might want, etc.

We have booked some nice apartments in Rome on airbnb. The last time we had a great 3BR unit for seven of us. The price was significantly lower than getting two or three hotel rooms.

Are you looking for a hotel AND an apartment?

Vatican and the Coliseum are at opposite ends of what might be considered the historic centre. Unless you have a reason for that you might want to also include the whole area in between.

Obviously the first week of May includes May 1st which is a national holiday in much of Europe. Are the dates fixed? I wouldn't wait too long for an apartment. Hotels have multiple rooms but apartments sell out easier.

Hotel Kennedy?

Hotel Aberdeen?

Both in Colesseum/ Termini area.

Thin

We stayed at Hotel Bolivar many years ago and loved it. Centrally located. Just looked at your dates aND 5 nights is $1031US. Beautiful old building, aND rooms. Check out their website
​​​bolivarhotel.eu.

Check out Hotel Spring House which is quite near the Vatican. Stayed there several years ago and enjoyed it, think it meets your criteria.

My husband and I stayed at Best Western Spring House in 2009? The hotel was fine as we stayed in the duplex room with retractable skylights. However, we did not really like the area.

Thin

Look at the Hotel Julia and Domus Julia.
We stayed there several years ago, and liked its location near the Spanish Steps. Very nIce breakfast included in a pretty dining room.
Our suite shared a full kitchen and dining room with another suite (but no one was checked into that suite, and we didn't need a kitchen).
I think it's in your budget.
https://www.hoteljulia.it

My favorite hotel in Rome is the Modigliani.

A few years ago we stayed at the Hotel Campo di Fiori and loved it. The room was small but the location was great. Nice buffet breakfast is included. We especially liked the rooftop terrace space that we had all to ourselves - perfect spot for a glass of wine or a picnic meal overlooking the rooftops of Rome.

We arranged a car service / airport pickup directly through the hotel which made our arrival into FCO then to hotel as easy as it gets.

Thanks for all of the suggestions. Now I need info for Venice. We will be spending 2 nights there at the end of our windstar cruise. Any hotel recommendations, again the same perimeters , under $200 per night, smaller place., not sure if i mentioned we also like staying in b and b's, as long as they are clean and updated. Also an other recommendations on restaurants, more out of the way less touristy places would be great. In

We stayed three nights in this little one-star hotel in Venice, recommended by Rick Steves several years ago.
It's a nice little boutique hotel, with a simple breakfast included. The hotel sits at a small canal, with singing gondoliers.
http://www.hotelriva.it/index.html

My daughter had stayed at this little hotel, but it's more out of the way:
https://www.casarezzonico.it/en

A few years ago we stayed at Hotel Teatro di Pompeo. It is in a very central location right by the Campo de Fiori. It's within your budget and still has good reviews on Tripadvisor. More recently we have opted for small apartments, but for only 5 days a hotel is probably a better idea.

DianePD - i think that with respect to the suggestions by MoBro, you probably want something a little closer to the station if you are only staying in Venice for 2 nights in which case the place that I usually stay at should fit the bill:

https://www.hotelarcadia.net

it's easily reached by vaporetto from either the Guglie stop on the Cannaregio canal or St Marcuola on the Grand Canal, is exceptionally friendly and does a great breakfast. Terrific value for the money. There are excellent restaurants along the side of the Cannaregio down towards Tre Archi.

Diane,

In Rome I recommend you check out Hotel Villa Pinciana, near the Borghese Gardens and Via Veneto https://www.hotelvillapinciana.com/en/ Its a small hotel which offers breakfast. Rooms are well appointed and have updated bathrooms. I've stayed there twice, last time this past September, and wouldnt hesitate staying there again. I just checked, and for your dates its around $180/night.

In Venice I recommend the B&B Al Ponte Mocenigo. https://www.alpontemocenigo.com/ Ive also stayed there twice. Lots of Venetian charm, yummy included breakfast, right off a vaporetto stop ( San Stae), which is not far from train station. This hotel is near the Rialto bridge, but away from the hustle and bustle of the areas overridden with tourists. There's a nice trattoria almost in front of hotel that its certainly not touristy. Forgot to add, in May rates at this hotel are less than $200/night

Good luck!

The Al Ponte Mocenigo does indeed look good and as you say very convenient for the San Stae stop. Also there are some very good restaurants nearby - the eponymous Osteria Mocenigo, which I ate at for the first time in January but will definitely be going back, the well known La Zucca, and Il Refolo where I've eaten twice and enjoyed it both times. In fact I spent a week in an apartment in this area last July and it was never that busy. Lots of neighbourhood shops and cafes and well off the normal tourist trail.