San Francisco is super casual about dress. You can wear pretty much anything you want anywhere. No one will turn you away. Cargo Pants and a Polo are going to mark you as a tourist, swap to jeans and a hoodie and they will just think you are a local.
Solo dining is not an issue at all. Its easy to get a seat at the counter of the in demand places. House of Prime Rib will have no issues for you. Just make a reservation for 1.
Try 5A5 steakhouse, Commonwealth. Anything that catches your eye on Valencia or Mission st.