I mostly agree with @Scott P..
On the one hand, doing a cash out refi is not a taxable event and gives you the cash to buy more property. Plus there is no time crunch as with a 1031.
However, if your goal is to build your portfolio closer to home, take advantage of this lapse in the lease and do a 1031. (personally, I have not problem investing out of my home market - see my tagline. But each investor has their own comfort level and if a nice nights sleep means a property close to home, do it. )
For a 1031, you have 45 days from settlement of your old property (relinquished property) to identify a replacement property or properties (not limited to a 1 for 1). And then 180 days from the settlement of the relinquished property to settle on the replacement property.
But here is the big, big rule to understand. If you identify a property within 45 days and it is scheduled to settle after those 45 days and something - anything - happens where you can't settle, you are out of luck. No second chances. Bad title, house burns to the ground - doesn't matter. Capital gains due on the relinquished property.
Yes you can identify more than one property and fall back to a 2nd or 3rd choice if deal one blows up but will they still be around?
Do ALL you can to settle within the 45 days so if it doesn't settle, you get a 2nd chance. You can probably start to look seriously once the relinquished property is under contract. Do it.
Again, a cash out refi has no time pressure.