I'm in Los Angeles, Detroit, in the Basin (West LA). A good location here too as we can walk to the shops, and DH gets the bus into work, so we actually use the car very little.
Don't worry. It'll be fine. If you can afford a taxi or a Lyft, I'd say it's probably a good idea. Then you'll be done after one trip, all your stuff around you, and you can start to relax, have a (non-alcoholic) beer to celebrate.
But if not, take it easy, so as to make sure you don't lose anything en route or leave anything behind (keys, phone, head...). Good luck! 