BotB

In terms of central location, the Sheraton would be best to get around of the three you mentioned. I have no idea how good it is but for location it is the best of the three. (Westin/Sheraton/DT). The DT was excellent as a hotel and restaurant but location was a bit out of the way. All locations would be safe and you will not have any issues that way. Even walking back late at night would be no worry, although the side streets going back to the DT are quite quiet at night with few pedestrians and you would have to go past the car park for the main train station which may get some dodgy activity later at night (we didn't encounter any issues though).

In any case, we walked extensively around the city centre (but the weather was good, if cool). The main areas to see are from the train station to the South up to the cathedral as the Northern boundary and just East of the Sheraton (where the Meštrovićev paviljon is located) to over around where the Westin is (as the Western boundary). The main shopping and pedestrian streets are up near the Cathedral and the museums and such are mostly to the West near the Westin from memory. The area around where the Cathedral is is hilly but the rest is flat. The cathedral area is very touristy and quaint but worth looking around.

Personally, I'd still go back to the DT due to the hotel quality and being a bit away from the main tourist area for some of my stay and then actually (a shock to say this on FT) stay at the Esplanade Zagreb Hotel for the days we wanted to be nearer to the centre. The Esplanade is a great piece of history and has its own charm at a very good price point.

If you do walk around the city within the area I mention and see most of the sites and stay at the DT, expect to do at least 10 Km (6 miles) to 16 Km (10 miles) a day though.

A great city and very inexpensive for food and drink. Enjoy ^ , hope this helps.