Trying to decide where to buy first property

[Lauren Andrea]

Hello everyone!

I'm new to real estate investing and Bigger Pockets. I'm having a difficult time deciding where to buy my first property. My goal is to buy a duplex (where I would live in one unit) or a house with a backyard big enough to build an ADU I could rent out (while I live in the house). I do not want to buy a fixer upper or a house that needs a ton of work for my first property.
I live in Los Angeles, which is obviously extremely expensive. I rent an apartment here for $2,600 a month. 
I need to be in Los Angeles for my career, so moving permanently is not an option at the moment. I can, however, travel occasionally. 
I'm planning to take out a conventional mortgage loan and have been pre-approved for a maximum of $675,000. Duplexes and houses with guest houses (that are in good condition and wouldn't need to be renovated) run around a minimum of $900,000 here, so that limits me to condos or single family houses under $675,000 (which generally need a ton of work). For this reason, I'm heavily considering buying in Atlanta instead. My parents live there so I spend a considerable amount of time there when I'm not working. Housing prices there are also way more reasonable for the type of property im looking for. I've seen multiple properties that are ideal for about $400,000, which is well below what I have been pre-approved for. An ADU would cost an additional $160,000, for a total of around $560,000. However, if I bought in Atlanta, I would need to continue to pay rent on my LA apartment because I would ultimately need to return to LA for work. 
My question is: should I buy a duplex (or a house with large a yard) in Atlanta, while continuing to have to pay my rent here in LA (which is $2,600)? 
Or, should I just buy a house with a large backyard here in LA for around $675,000 (and wait to save more money to build a ADU) and no longer have to pay rent?

Thank you so much in advance!