There are so many hotels in the downtown area, but listed below are a few that Jim and I can heartily recommend. Most, if not all, have courtesy shuttles that will take you to Union Station (our wedding venue). Three hotels that we can see from our living room windows are:
Little Tokyo has a lot of restaurants, shops, and museums that are within a short walking distance (like, right outside the hotel doors). I heartily recommend walking to Fiore's for Italian yogurt (Japanese Village Plaza). The Miyako Hotel, which is a block east of the New Otani, costs about half of what a room at the New Otani does, and is surrounded by more restaurant options. The Biltmore is a block and a half away from a subway stop (which can take you to Union Station and beyond) and across the street from the Central Library.
Other downtown hotels we can recommend:
If there are other hotels in Los Angeles that you are considering staying at, leave it here in the comments and we can update this post with more information about that hotel and the surrounding area.