Any ideas/websites where I can find a gender neutral coming home outfit for July???

Try Kohl's, they have a nice baby section. Also, your department stores such as Macy's or Boscov's.  Boscov's has a nice selection and there is always some kind of sale going on infants and kids clothing. I bet Target has some good things as well. I hope this helps. 

Another thing to consider, you may want to choose one of the outfits that you receive at your shower. I got so many cute things at both of mine that I am planning to pick 2 from those items ( a smaller and bigger size since I don't know how big the baby will be).

I second the Kohl's - I just got a bunch of cheap outifts on sale. Also baby gap has some cute stuff too and if you can get it on sale the prices arent that bad.