The garage is pretty much a must-have for me. Check out The Highlands at Montour Run in North Fayette Township, Ventana Hills in Robinson Township, The Polo Club in Moon Township, Waterford Landing in Moon Township.

Some newer condos to rent in the west suburbs probably offer a garage (not attached) to rent but will charge extra per month for that. You will find that apartments and maybe even condos will be cheaper to rent. It would almost be cheaper to buy a house with these things than to rent, in some cases. Unfortunately, the amenities you're looking for (2-3 bedrooms & a garage) pretty much constitutes a house. However, a difference is new housing (and property taxes) in the suburbs here is much more expensive than it is in the Cleveland/Akron area. I lived in NE Ohio for years and you will probably like it here. Consider contacting real estate agents of ones for sale and ask if the owner would be willing to rent instead of sell. There are lots of townhouse communities in the Airport/Robinson area. Those are all I can think of off the top of my head.

drive through Canterbury Commons in Moon Township, Hawthorne Village in North Fayette Township, Walden Woods in North Fayette Township, Pleasant View Estates in Robinson Township, Pennsbury Village in Robinson Township, Independence Square in Hopewell Township (Beaver County). Since you're only in NE Ohio, if you get a chance to come drive around. People are still old-fashioned in the sense that they post a 'FOR RENT' sign in the window/yard more often than posting on craigslist and other mediums. A lot of times around the area, you have to drive around to find things to rent.

Polo club moon township