If you're looking for great oatmeal, there aren't many options in walking distance of the St. Regis. Best bet is probably Blue Bottle Cafe in Mint Plaza. Highly recommended for the coffee, and the breakfast is pretty good, and they do have oatmeal.
You might also look into the Grove Cafe, at the corner of Third and Mission. I don't offhand know whether they serve oatmeal, but it's possible. Breakfast food there is decent, though not great. I'd advise the French toast. Egg dishes tend to be somewhat bland.
Note that the St. Regis is a couple of blocks from the Montgomery St. BART and Muni station, so you can get to much of the city and East Bay without walking all that far. I can't personally correlate great oatmeal with BART/Muni stops, but someone else here might be able to do so. Or you could search for "oatmeal" on this board and do the correlation yourself.
Blue Bottle Cafe
66 Mint St, San Francisco, CA 94103
Not sure how far you're willing to go but I hear Farm to Table is great. Ironside also serves breakfast. Perhaps, the Butler and the Chef Bistro. If you're doing a weekend brunch, Universal Cafe is very good.
2814 19th St, San Francisco, CA 94110
Butler & the Chef Bistro
155 S Park St, San Francisco, CA 94107
754 Post St, San Francisco, CA
680 2nd St, San Francisco, CA 94107