Local Information
Food Options
Downtown Los Angeles has seen a major renaissance in restaurants over the past 10-15 years. There are many excellent restaurants within a short walk or ride of the hotel, and Yelp/Google will find them.
If you are looking for relatively fast options for lunch, two natural choices are California Plaza and Grand Central Market. California Plaza is immediately next to the hotel and has a handful of lunch-oriented eateries. Grand Central Market is a few minutes walking down (and later back up) Beacon Hill, or you can ride Angels Flight. It is a historic and very large food court and market, with dozens of eateries of different ethnicities.
Chinatown is about a mile from the hotel, and has a variety of low-key options, including some acceptable Chinese food. (The more authentic Chinese food is to be had in Alhambra/San Gabriel, which is quite a bit further.)
Little Tokyo is also not too far from the hotel, and has a large number of good Sushi places, including a very good vegan "sushi" place called Shojin. Speaking of vegan, the vegan restaurant "Au Lac" is close to the hotel and serves very good vegan Vietnamese-inspired food.
Things To Do
The downtown LA renaissance extends beyond food, and there are numerous entertainment and tourism options near the hotel.
The hotel is a very short walk to Disney Hall (home of the LA Phil), and the Music Center (which has three theaters, including stage non-music performances). The STOC dates are a bit outside of the season for these venues, though there are some events happening. On the adjacent weekends, there are events at the famous Hollywood Bowl, a beautiful and traditional outdoor performance venue (reachable by Red Line).
Downtown Los Angeles still has a lot of beautiful early 20th century architecture, in particular Beaux Arts and Art Deco buildings. If you get there early enough, the LA Conservancy leads guided walking tours on Saturday mornings. If you are exploring on your own, make sure not to miss the impressive lobby of the Bradbury Building (open 9:00-5:00/6:00), and check out the Southern California Edison Company Building and the Los Angeles Public Library, all very close to the hotel.
The Staples Center and LA Live are a short ride (or long-ish walk) from the hotel. Staples Center is the home of the Lakers, Clippers, and Kings, among others. LA Live hosts many concerts and other performances.
The Angels Flight railway is right next to the hotel, and one of LA's famous landmarks. It will be hard to miss. Grand Central Market (see above) is another famous landmark itself.
There are several museums close to the hotel. In particular, the Broad Museum is very close to the hotel, and has very "Instagram-friendly" collections. Admission is free, but you need to make reservations ahead of time; for weekends, this means several months in advance - on weekdays, you can sometimes get in with just a few days' advance notice.
If you are interested in unusual art, you may want to check out the Watts Towers. The Blue Line takes you there directly in about 25 minutes.
There is much more to do, but search engines will help you find those.
Safety in downtown Los Angeles has improved dramatically over the last two decades, and most of it is now quite safe to walk, though like all major US cities, it does have a non-trivial crime rate. One area you probably want to steer clear of is Skid Row, between Main and Alameda, and 3rd and 7th Streets. Skid Row has the largest number of homeless anywhere in the US, and corresponding rates of property and related crimes. It should be easy to avoid it, as it is not really on your path to any place you'd normally want to reach.