Hi @Howdini,
Welcome to L.A.! 
@PorkyBelly has a good list already. Adding some thoughts and links (with pics) for you below:
Silver Lake
- Night + Market Song
- Pailin (Northern Thai) - Not in Silver Lake but close by.
- Broken Spanish - Modern Mexican done right.
- Kismet - California + Israeli that’s vegetable centric and with great sourcing.
UCLA or nearby
-
Shamshiri Grill - Persian deliciousness - Get their Stewed Lamb Shank (and they have vegetarian and vegan options as well).
Since you’re on the Westside already for UCLA, you could try some of the places @PorkyBelly listed on your Thursday section on this day, depending on when you start / finish your visit. 
But either way, some links:
- Gjusta - Just awesome. Look at the link for lots of pics and descriptions of dishes.
- Gjelina - More of a sit-down sister restaurant to Gjusta, totally different menu, great California-driven produce, farm-to-table, etc.
- Felix - See @PorkyBelly’s link above, here are more pics from my visits.
Hope this helps!