Hi. I live in Fort Collins which is very close to greeley. I am the same age as both of you.
My boyfriend and I have been in a similar position to move! We were both raised here so we detest it for various reasons haha we are moving to the Northwest.
BUT it is a wonderful place to live for many people
I highly recommend Fort collins over Greeley (I live in the rural area of Laporte to be exact but it takes about five-ten minutes to drive into the main part of Fort Collins, that's ideal because Laporte is way cheaper than rent in Fort Collins)
fort collins has tons of amazing activities going on constantly. they have lovely parks, a great Oldtown shopping center with unique stores and artists. CSU is there so it's a college town. there's great meetups if you want to meet new people.
CSU apparently has an amazing vet program that you may want to look into.
the humane society here and the FCC (fort collins cat rescue) and Animal House are wonderful places that I've volunteered at previously. there's also horse rescues and I bet there's far more animal-wise you can find here.
also, my favorite part is driving into the Poudre Canyon (it is so beautiful!) hiking and camping is definitely a must here (unless you're not into that haha)
I personally dislike Greeley because it just doesn't have the same comfortable feel to it for some reason, it also doesn't have the same access to the mountains (it will take you longer to drive there) you may have an entirely different experience.
also, from fort collins you can take a 45 min drive or so to visit the Shambhala Mountain Center which is absolutely stunning and really peaceful and wonderful safe haven in the mountains - you can hike up (to visit the great stupa which is this wonderful buddhist temple, it is so stunning in person pictures online don't do it justice), my family isn't buddhist but we go there all the time - they have a bunch of amazing programs there too
sorry for all the random information, not precisely sure what I should mention
Fort Collins is a lovely place with a ton of things to do, and I recommend living just outside of it if you can't afford rent there
if you have any questions feel free to ask/PM me :)