Whether or not pets are permitted could be a building and/or individual unit owner policy. There will also be limitiations on weight in many cases. Best bet is to work with an experienced leasing agent who can set up a good search so you don't waste your time.
Interview three "leasing agents" and let them know what you are looking to lease. Find out if they have any experience in the Pilsen. I do suggest you meet at La Catarina Cafe, it's quite comfortable. Good luck!