You can usually find a local property management company in any city. Before calling anyone, do a Google search on the company or try to get a reference. There are plenty of property management companies, and there are plenty that don't do a good job. That's the honest truth.
I wish you the best!
The Austin Rental House Specialist!
It is imperative that you get a very good property manager... then it is just as important that you have someone to be your eyes & ears (family or very close friend).
It can and has been done with great success, but you cannot just leave and check up now & again. You need good follow-up & communication with whomever you hire. Check their references & check the people they've got working for them.
I will echo Paul in saying that you need a full time property manager. They are out there - via the traditional real estate agency to the commercial/residential property management exclusive companies.
It depends how long will you be gone and when you return will it be the this city? What is you equity position. Will the rental income cover your mortgage payment, taxes and insurance. Allow for a vacancy before making a decision.
I would have it professionally managed since you are going to be out of the country.
I'm an investor so I don't believe in selling when everyone is selling. I believe in selling when everyone is buying. Austin's market doesn't appear to be taking as hard of hit as other markets in the country but if selling is your other option make sure it makes sense in the current market or otherwise hold onto it and see my comment about tax free capital gains below.
Another consideration is will you be returning to Austin anytime soon (1-3yrs) or is this an indefinite move. If you don't plan on being abroad long and will return to Austin you might hold onto the property and coordinate your lease(s) with your estimated return so you have a home when you come back. Especially if you've got good real estate in Austin. Odds are if it is good real estate it isn't going to be cheaper the next time you buy it.
Lastly, if your unsure about returning to Austin and/or when. If you've lived in the house the last 2 years then you got 3 more years to play with in terms of your profit being tax free. IRS says you get a capital gains exclusion on your homestead up to $250k a person or $500k married couple if you've lived in the house the last 2 of 5 years from date of sale. Rules are strict on this so make sure you talk to your CPA. If you rent look at it this way you won't find a 401k plan to match.
Make sure your cash flow makes sense and then find a reputable property manager and price it to rent. I'd suggest getting as many referrals as possible on a property managers, interview at least 3 and call their referrals.
Enjoy your time abroad!