live downtown or east liberty?

Hey all! I moved here recently from a big city on the west coast and am looking for an apartment. I work in oakland and am a single woman with a dog.

I've been apartment hunting lately and just wanted some opinions. I found an apartment in East Liberty that I love due to the layout and location, but it's at the top of what I'd want to spend in rent. I love that it's in a walkable area and near coffee shops, grocery stores, and on a bus line especially since I'm uncomfortable driving in snow or bad weather. While I'd love to just jump on it and commit, I also want to consider more cost-friendly options and was recommended looking downtown by a friend. I found that comparable apartments there can be $600-$1000 cheaper than the East Liberty apartment, even including a parking pass.

Since I'm new to the city, I was curious on what everyone thinks about living downtown. Is it safe for me to walk my dog around at night? What's it like to be there and how's the transit? I'm more drawn to places that are walkable and have lots to do, as I don't prefer driving in general and like to take my dog when I go places. Thanks for your time, any insight is helpful.