I agree with Matt in regards to those areas. Another thing to keep in mind, if you are looking to buy and hold, areas such as Cleveland Heights, University Heights, Shaker Heights, Beachwood all have very high property taxes so its going to eat into your cash flow a good bit. I know a lot of guys buying, rehabbing and flipping in the Cleveland Heights, University Heights areas as the city is generally a good area to raise a family (except some pockets which are really not good areas) and there still are plenty of homes to be found for good prices the can be cleaned up and sold for a good profit. If you move further out such as Mayfield Heights, Lyndhurst, Parma, Bedford, Euclid, South Euclid, you will find the taxes are a bit more manageable. Keep your eye on Little Italy as its a little pocket of town that holds its value really well because of its history and culture, yet because its in the city of Cleveland, the taxes are low (in relative terms) and its mostly multifamily homes. It brushes up with some rough areas but given its strong Italian Heritage, the town does a good job of keeping the unwanted out. Im doing a loan for a client on 6 unit right off the main strip and even at $200k, the taxes were only about $100/month and its a high demand area so there's really good cash flow for a 6 unit.
On the West side, the Tremont fad I would say is already in full swing as you can make the argument that it was part of the beginning of the resurgence of the West Side in the last 5-10 years. Prices are already up and with Ohio City and West 25th coming along, it's still growing but kind of hitting a wall because other options are opening up for the yuppie crowd. You should also look at Gordon Square and the Battery Park area. Those are upcoming areas that were kind of hidden gems that have seen good development but not much publicity. However, the city has been doing a major redesign of the shoreway/Rt.2 which runs just north of Gordon Square, and right now they are knocking out a huge hole in the bluff that used to separate Gordon Square from Rt. 2 and they are adding a whole new entrance/exit which will allow direct access to the area right off Rt. 2. They just finished the over pass for that entrance and it has GORDON SQUARE in huge letters so I would say that's pretty good publicity. Most importantly, on the other side of Rt. 2 is Edgewater Park which is the only beach in town (Cleveland proper) that's about to get a 1.5 million dollar beach house. So basically if you live in, or near, Gordon Square, you can walk out your front door, get on your bike and be at the beach in about 5 minutes. Crime is a drawback though because of its surroundings, however, I drive through there every day for work and not a day goes by where you don't see hang gliders, para sailing, SUP boarders, dogs, runners, bikers... Its a very active area that the Metroparks have really transformed in recent years....
Anyways, that's my 2 cents....