I think my #1 thing would be pest problems. Look at online reviews, ask prospective neighbors if you can. If there is overwhelming consensus of Bugs Everywhere, I stay away. It's not considered a valid reason to break a lease, and if landperson/manager is not on top of it, it can be miserable (bf had this). Even nice looking places can have these problems! Granite countertops and SS appliances have higher ROI than pest control (at least short term)...
(On the other hand, dont take reviews too seriously; people love to complain. Nature gets inside sometimes...you just can't take care of a building-wide infestation by yourself, not worth the risk IMO.)
Obviously, look at neighborhood. There are websites like CrimeReports.com, NeighborhoodScout.com, and Niche.com that can help suss those things out. Though, if you aren't moving far, you probably know this about your local area.
Think about whether you want top floor (possibly safer from break-ins, quieter for kid's naps) or ground (not worrying about kid running around on neighbors heads!) Although you may not get much choice. People do live with both.
Other than all that...just look at everything and don't be shy. Turn on taps, open cabinets, etc. Come up with a list of questions in advance so you don't forget (Laundry? Parking? What utilities are included? How frequent is trash removal? What happens if my drain clogs/pipe leaks/furnace dies at 11pm on a Saturday?)
Most of all: it will be fine. My parents rented my whole childhood (and still do). I've rented my whole adult life so far. Plenty of good people rent, plenty of people with kids rent. <3 Good luck!