My husband and I are close to completing the renovations on our first rental property and will be moving into the refinancing portion.  My question is around the appraisal and where we should be focusing money.  Does anyone in the DFW Market have insight as to what a bank appraiser is mainly going to be looking at?

It would be a good idea to talk to or hire your own appraiser and make sure you are doing the things to get a top appraisal. Then leave your appraisal in the property for the bank appraiser to see / leverage. You have just made his job easier and he will likely take the easy route and use a lot of what you have provided towards the highest appraisal you can get.

Sure, I've done dozens of these appraisals in the last decade in your area.  Here are a few tips.  (nothing really original here)  First, give the appraiser a list of repairs and total amount spent.  Shows you actually did something to justify new value.  Second, kitchen is where I've found you get biggest bang for buck, particularly if you put in a solid surface (I do commercial grade granite and it helps every time).  Third, make it easy for the appraiser to get in there.  Don't make them schedule with the tenant directly as it never works.  I usually have my maintenance man do it.  Fourth, recognize they are going to be more conservative on refis vs. purchases.  Nothing to really do about it, just the way it is.   Fifth, you can give them comps if you want, but I've never found that very helpful unless it's a weird neighborhood with a wide range of values.  

Kitchen and bathrooms are almost always the best focus here. As mentioned above a by @JohnChapman a complete record of all repairs or renovations is also good I think. I try to leave my maintenance/warranty files for them as well as all manuals etc. This shows a thorough and complete record of what's been done and in my experience it is always rewarded in a more favourable manner.

Thanks everyone for your responses, all of that will certainly help us in completing this last phase!