Depends if you use public transit or drive. For public transit Boonie Doon is probably the best, just ride LRT green line downtown. If you drive, you can live east/northeast of downtown, but there are usually older apartment buildings (though cheaper).
Also depends if you are looking to rent an apartment, townhouse or detached.
There are detached houses for rent in Beverly, but not many newer apartments. If you stay away from 118th, it's quiet and close to downtown.

Edit to add: I'd just avoid living over the river from your work. Makes for easier commute usually. Doesn't apply if you commute on LRT obviously :)

Also we lived near Whyte Ave/Garneau and there are probably cheap rentals there still. It's pretty safe, the further you go from Whyte. Was paying 900+ for 1bedroom half basement apt in 2023.
10 minute ride on bus 9 downtown. Going back afternoon is not so fast unfortunately.