First i must say that i haven't lived in Cinti for five years. However i still make the occasional trip and know some who live there still.
I would never compare OTR to Tremont. There isn't a comparison for OTR to a Cleveland neighborhood. It is a good sized neighborhood north of the CBD. The shared border with the CBD is an eight or ten lane divided road that used to be the canal (or the "Rhine") that ran through the city from the I-75 corridor. You know when you've left the CBD when office buildings are replaced with fantastic Victorian row houses that are rotting from the inside out.
Obviously it was a major German neighborhood (but really what wasn't in Cinti?) years ago and has since become generally a place for poor African Americans and Appalachians. It definitely has the worst rep in the city (even though i would be far more concerned about walking through the west end or at people's corner) and while there was some money made on Main St with the night life during the turn of the last century, that is certainly on the down slide... but definitely just one street of "development" which really didn't do much in the way of rehab and sent rents through the roof along Main for crappy old units. And nothing at all like the Warehouse District that is a neighborhood within the CBD and has a booming housing market. Did you know that the Warehouse District is completely rehabbed at this time? Anyway, with the exception of Pendelton (a sub neighborhood within OTR that doesn't want to be associated with OTR) i really wouldn't spend to much time down there myself except at the market when open or at the music hall when there's a show. Which is a real shame because it really is a beautiful example of urban design with a fantastic park and one of the largest collections of Victorian age housing.
I'd hate to say it, but everything i see and hear points to OTR sliding further since the riots a few back. In closing i would say that i would venture into OTR on foot if i had a reason, but i wouldn't take the lady friend (ie my wife) or some kids. I would definitely be conscious of my surroundings. But in the end only those of us into urban spaces would be interested in seeing this part of town. And while it isn't as bad as everyone thinks in the square exurban world, it is still pretty bad.