There are great walking tours of the downtown LA area run by knowledgeable staff at a very reasonable price. We've taken their Old And New LA Downtown and their Chinatown and Japantown tours. Here's the link www.dtlawalkingtours.com/.
To be honest, there's enough to see and do in the immediate area of the station that I wouldn't bother with the HOHO bus tours if you only have one day. (And I am generally a fan of them as a quick orientation to a town). LA is pretty spread out, so the HOHO sights are less condensed than in a typical HOHO tour.
Olvera st (directly across from LAUS) is touristy, sure, but the stalls are photogenic (and we bought a frilly Mexican dress and fancy fan for our 4 year old granddaughter that she absolutely loved!). There are several Mexican restaurants there that are just what you'd imagine they are, but to my mind, the can't miss eat there is the Mr Churro stand, where you can get freshly made churros that will spoil you forever. They also do a pretty mean breakfast burrito. Olvera St is the site of the oldest non-native settlement in LA, and the oldest surviving house still stands and can be visited--it's filled with period furniture and accessories.
MOCA and the Broad Museum are in the neighborhood, too, if you enjoy modern art. The Broad is free (yay!) but you have to book in advance (boo!) by logging onto their website on the first day of the month before you plan to visit. There's also a standby line, I believe. Honestly, I always mean to go there when I'm traveling through Union Station but I forget to get tickets in advance, and at this point in my life, I'm not standing in line for much of anything.
Want a great and unobstructed view of the downtown area? Head for the free observation deck at the iconic City Hall Building. Open normal business hours.
Also, no railfan will want to miss the Angel's Flight funicular, adjacent to the Grand Central Market. It touts itself as the world's shortest railway, and it's finally running again.
