Hey Librado! Long time DFW apartment locator here! Hope it's a great weekend, and congrats on the move. I've run a ton of searches for apartments in the $1000 to $1300 range in the North Dallas/Far North Dallas area for my peeps. These are the 8 go-to's that I usually start with when looking for 1BRs $1050-$1200/month:

75 West - 1BRs starting at $1285 plus rent special (net rent mid $1100s) - https://live75west.com/

Prairie Crossing - 1BRs starting at $1176 plus rent special if you lease within 24hrs of touring - https://www.liveatprairiecrossing.com/

City North - 1BRs starting at $1174 (plus rent specials on some units) - https://www.citynorth-apts.com/

Sola Galleria - smaller 1BRs starting in the $1180-$1280 range (plus specials on some units) - https://solagalleria.com/

Alvista Galleria - studios starting at $1150, 1BRs at $1320 (plus specials on some units) - https://www.alvistagalleria.com/

Vail Village Club - smaller 1BRs start $1035, mid size 1BRs at $1185 - https://www.vailvillageclubapts.com/

Vail Quarters - 1BRs starting at $1040 - https://www.harborgroupmanagement.com/apartments/tx/dallas/vail-quarters

Keller Springs Crossing - 1BRs starting at $1250 - https://www.harborgroupmanagement.com/apartments/tx/carrollton/keller-springs-crossing

Hope that helps!! Feel free to give me a shout anytime to have a full search run for best units for your move-time, or to ask any questions about your move/apt-search that I could help out with. DMs always open and my help is always free of charge :)

Have a great move!