What's the best neighborhood in Shaker Heights for a first time visitor?

There really aren't any hotels in Shaker Heights as it's a very residential community.  Having hosted two weddings and some reunions we put folks up at the Chagrin & I-271 interchange  where there are lots of hotels to choose from.  None of them are within walking distance to Shaker so you will need a rental car.  There isn't much close by except hotels and restaurants and some shopping.  

It all depends on what you need.  There is a Residence Inn Cleveland Beachwood if you're having a longer stay and want a kitchen.  We've always been happy with the Hilton Garden Inn Cleveland Downtownc, which also has mini kitchens.   We have an almost brand-new Aloft Cleveland Downtown which is popular with the younger crowd.  

There is also a wonderful little boutique hotel at University Circle(where all the museums and Case Western Reserve University are located) called Glidden House.  it's a bit further away (maybe a mile) but there is so much to do there and The Cleveland Museum of Art is free all day, every day and it is one of the top museums in the world.  Lots of restaurants and activities nearby.

Hope this helps! 

A fun option would be to stay downtown, or perhaps at the well-reviewed The Cleveland Hostel in Cleveland's Market District.  RTA day passes are $5 and SH is served by both the Blue and Green rail rapid lines.

See "Lodging" here.  Also, read the Dining article for Shaker Square.

http://www.tripadvisor.com/Travel-g50207-c198218/Cleveland:Ohio:Tips.For.Visiting.Cleveland.html

http://www.tripadvisor.com/Hotels-g50959-Shaker_Heights_Ohio-Hotels.html

Fire Food & Drink, Balaton Restaurant, EDWINS Leadership & Restaurant Institute, Melt Bar & Grilled, Shuhei, and Jack's Deli and Restaurant all are great and popular choices.  Only Shuhei is directly in SH, but the first three are in Shaker Square, part of the SH school district even though in Cleveland.  The other two are in adjacent Cleveland Heights.