We stayed on Queen Mary a few years ago, as I am a liner history nut. While she has undergone considerable changes, there is still enough history here and there to get the liner feel. I strongly suggest that you splurge on a nicer room. We stayed in what was previously a suite on Mary and it was amazing. The bathroom even had the hot salt/cold salt water faucets in place, although non-operational.
Should you decide to go on a guided tour of Mary, I suggest the history tour and/or the World War II tour. (She served as a troop ship, and I learned a lot.) I wouldn't bother with the haunted ship tour -- lots of hype, little substance. Staying on Mary also gives you free access to the museum, that you can do on your own. Don't miss the engine rooms and the displays on the lower decks.
We took Execucar, a division of SuperShuttle, from LAX to the hotel. You can find quotes for both on supershuttle.com. On embarkation day, we took a taxi to San Pedro... I don't recall the cost.
A couple of years later, we stayed at the Pan Pacific, which towers over Canada Place. Pricey, yet so wonderfully located. There's a food court in the lower lobby of the hotel that saved us quite a bit of $$ on meals.