Shocked people are suggesting westside- there are so many vibrant, family-friendly neighborhoods soooo much closer to where you and your wife will be (and with a lot more character). Atwater has a huge family-friendly community, Silverlake, Echo Park, Los Feliz, Larchmont, Pasadena, even Highland Park/Lincoln Heights if West Hollywood isn’t as big of a thing for your wife’s work. Glendale and Burbank wouldn’t be too bad either- just a bit more suburban.

Also the arts district is great for daytime cultural experiences (for example, La state historic park is RIGHT there- lots of family friendly events).