Hi, the Roosevelt is a great hotel. I love tha cabana rooms by the pool. It has great lobby bar for people watching and it's right across the street from Grauman's and the Kodak theater. But if your plan is to check out the Strip than I think you're better of at the Grafton or the other Strip hotels mentioned. It's fairly safe around there and you walk to most of the bars and restaurants. The Grafton is decorated really cool and they have great pool that looks out over the city. When you stay on the strip you really feel like you are "in the middle of it all" if you know what I mean. Lots of beautiful people, fancy cars the whole "hollywood" thing. It can be a little much but it's fun to check it out. The Roosevelt is great because of it's old Hollywood feel but it's smack dab in the middle the tour bus tourist scene.
I don't know about the hotels in Beverly Hills but West Hollywood is very close to Beverly Hills. The Grafton is probably 5 to 10 minutes away.