I was born in Cleveland and although I haven't lived there since 1997, I still visit my family there regularly. My best friend lives there too and we both love Indian food, so when I am in town we indulge.
Our favorite restaurant is Jaipur Junction on Sprague Road at the corner of York Road. It's in North Royalton, near the Parma border. It's a small place that does a lot of takeout, but they do have tables. They serve on disposable dishes even for dine-in. Many Indian people eat there. The place isn't the cleanest, though - their bathroom is sometimes downright filthy. But the food is so good it keeps us coming back.
We've been to Udupi in Parma Heights a couple of times too but just don't like the food there as much. It's not bad, but we like Jaipur better.
We have also been to a place in North Olmstead a few times. It's on Brookpark Extension. I don't recall the name - it has changed so many times.
Another great place that unfortunately no longer exists was the Clay Oven in Fairview Park.
A couple of places that other people rave about but didn't impress us are Saffron Patch and Cafe Tandoor, both on the East side. I believe Cafe Tandoor has a location in Westlake now but I have not tried it.
Someone else mentioned a place on Wilson Mills Road - I believe it's called Maharaja. I went there once years ago and thought it was okay.
If you are willing to drive out of the Cleveland area, the Raj Mahal in Cuyahoga Falls is also good.
Hope this helps.
I'm a former Clevelander and here are my thoughts. Cafe Tandoor is ok, but inconsistent. I used to live very close by, so we ate it a lot out of convenience. I like the food at Saffron Patch, but the service is horrible. Before I left, I had taken to ordering delivery from a place on Wilson Mills that I am blanking on the name. Really liked it. I've heard good things about Udupi. Never made it to the west side to try it, though. There is a woman in the food court in the Colonial Arcade downtown who makes some decent homemade tasting food at lunch time. I think her stand is called Indies.
Udupi is in an unassuming location in a strip mall in Parma Heights. It looks like "huh? there's good food here?" but it IS good, albeit all vegetarian as the other poster said.
You could also try Cafe Tandoor as the other person mentioned. I think it's worth trying and you can make up your own mind. I am not a big Indian food person so I rarely go there but the times I've been there have been pretty good. It is in Westlake in the plaza on Detroit across from Crocker Park, where the Caribou coffee and sears hardware store are.
there is also the original location, on south taylor in cleveland heights.
i like saffron patch for the seafood dishes, some of the more street food-y appetizers, and the tandoor items. however (and this might sound a bit odd), i have to qualify my rec by saying that it's best not to go on a saturday night. a busy, full dining room plus the weekend demands of their catering business means that the quality of the food suffers.
sorry to say Indian is not a strong point around here. Of the ones I have tried, I like Saffron Patch in Shaker Heights the most. The Indian people I know tend to agree, although they said the best is cooked at home. They also mention Udupi Cafe in Parma Heights which is all vegetarian. I have not been here so I cannot comment. I have been to India Garden on the westside in Lakewood (ok I guess. I still am a repeat customer though), and Tandoor Garden in Cleveland Heights (also westside location somehwere). I have been several times and just do not care for it. The food tastes too rewarmed-from- the-cooler for my tastes.
edit: not sure if it is worth traveling far to any of above!