Can I get an unlocked phone instead of upgrading?

I currently have an iPhone 6 to go along with my AT&T wireless plan. For reason I don't need to get into, I'd rather not upgrade my phone through AT&T. My question is, can I just go into Best Buy or online and buy an unlocked iPhone X (for example) and just put my iPhone 6 SIM card into the new phone, then use a backup saved on my computer? Will this transfer service and everything onto the new phone without any issues?

Not sure but you can buy an iPhonex unlocked. Might as well go to Apple store cause it's the same price.

If it were an Android it'd be a little simpler…

You should be able to back up your phone and then restore it without issue. Once you've set the new phone up with your old SIM in it Almost everything should work straight off!

The one thing that can go wrong is conventional texting - you may need call an automated service to have AT&T send a code to your phone that will install the texting settings for you! If you don't do this iMessage will work fine, but you may not be able to send or receive conventional texts.

On a side note, if you've been paying for a phone on your plan, then switching to a SIM only deal can save you a fortune!

Use iTunes to do the transfer.