we always use 

http://www.booking.com/

be wary though, hotels in the city close to the Colleseum, Trevi fountain, spanish steps etc , like many Europena cities, have fairly small rooms and toilets.

Also many do not have lifts - so make sure you check the room layout and facilities thoroughly

https://www.google.com.au/search?q=Italy+Rome%2B+seniors&ie=utf-8&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&gws_rd=cr

https://www.google.com.au/search?q=Italy+Venice%2BSeniors&ie=utf-8&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&gws_rd=cr

A good start would be to trawl through these links and glean some good info.  Plus could check on Smart Traveller gov site for any warnings just before departure. Italy is safe enough I have found but not been for a few years and Venice is lovely but expensive I usually transitioned through to catch the ferry over to Cyprus which is also a good place to visit and cheaper. Ferries used by locals not usually see adverts for tourists. Lots of Brits live there these days retirees. Along with Germans.

Have a lovely trip.

Shenna. 

Rome

 There are many good three star  hotels close to the Termini Rail Station.         I  never found a bad one.

I recommend........Hotel Romae   Cheaper to book through Venere than to book direct. Trust me, I checked this out when I arrived at Hotel Romae.   Tis so.

http://www.venere.com/hotels/rome/hotel-romae/

Venice

Well hotels in Venice are expensive.   And the hotels are pokey, and Venice is DEAD after sundown.

 Look to stay in the Lido area, it's the best choice I recon for folk of your age.  Stay in a good hotel in the Lido , and catch the ferry to St Marks in the morning.

 or, my choice,  Chioggia.  

Stay in Chioggia, a ferry ride from Venice  Check it out. It's like Venice without the tourists.  V good for oldies. The central area comes alive after sundown, with the passegiata,  young folk gravitate to theit end of the strip, the oldies at the other , each to find their favourite apperitif at their favourite caffe/bar.

Phil.

The Travel bug could take hold reading these suggestions!!!!!!!!