$1400-$1500 for rent in St. Louis City? Really? That's your problem. Do you need granite and 4 bedrooms now that you have a baby? There are many great areas of town that you can rent for less than that and many good areas you can rent a house for nearly half of that (I know because I rent them out)!
If it's just you, wife & baby; a 2 bedroom apartment could easily be had for less than $1000 in Dogtown, west of Hampton, West of Kingshighway, Shaw, Holly Hills, Carondelet, St. Louis Hills, Tower Grove South, The Hill and all of those are great areas and a good place for a family. You could find many apartments for around $800 in most of those areas. If you want a house, you could probably rent a house for less than $1400 in in each of those areas as well. I have several houses in good parts of Dutchtown that border some of those great areas that rent for $750-$900.
Safety is a feeling. Look at actual numbers and statistics. Come to the understanding that bad stuff can happen anywhere-randomness (even the County). And then you will realize there are actually few places in the city where bad stuff is common.
My guess, is that with your quote of $1400-$1500 for rent, is that big and/or trendy is important to you. The only way that trendy pays off in St. Louis is if you can walk or ride your bike everywhere and are saving $600-$700/month on not having car payments/insurance/gas/car repair expenses.
If you truly want to get into REI and out of the rat race, you're going to have to get out of the rat race and start saving money. Fortunately St. Louis offers a wide selection of affordable rental options.