if you plan on staying in Beverly Hills and not venturing out into the surrounding areas then i suppose you could manage by walking or taking the public trolley that has a very limited operating schedule and route.  However,  if you want to see the actual hills in Beverly Hills you will need a car.  Los Angeles and Beverly Hills are car cities.  We have a public bus system but it isn't easy to use.

 

Beverly Hills is itself relatively small.  It is divided into three sections- south of Wilshire, Wilshire to Sunset Blvd., and north of Sunset Blvd.  South of Wilshire is mostly residential except for Beverly Boulevard. Wilshire to Sunset is comprised of the famous shopping district including Rodeo Drive and also of what is called "The Flats".  The Flats is the residential area of mansions, though many are now McMansions.  These streets are laid out like a grid. if you travel north on any of them you will eventually hit Sunset boulevard.  If you travel south you'll hit Santa Monica boulevard.  North of the flats is Sunset boulevard and the hills.  This is where the true mansions of the city are nestled.  Also the Beverly Hills Hotel is  north of Sunset and unless you are in great shape, you need a car to get there.

Parking is expensive in beverly hills at any hotel.  Be prepared to pay more than $20.00 per day.  If you are just visiting for the day there are public lots throughout the commercial part of the city.  i believe the first 2 hours are free though there was a change in policy recently and it may be only the first hour free.  A good alternative is to bring a roll of quarters and park at any of the public lots that border Santa Monica Boulevard. It ends up being a lot cheaper as even with the 1-2 hours free the next hour or fraction of is pretty expensive. There is an especially good lot on Little Santa Monica and Cannon in the parking lot of the old brick Post office.  There are usually spaces avail;able there.

Here is a link to a map of the parking possibilities in Beverly Hills.