One of Cleveland's original "streetcar suburbs," Lakewood was built and settled primarily in the late 19th and early 20th centuries. Most of its existing housing stock was built in this timeframe, and is surprisingly well maintained. Lakewood has managed to retain many of the best features of a city, small town, and suburb, and scenes reminiscent of all three can easily be found within a few blocks of downtown Lakewood (Detroit Ave. between Cook and Bunts) as well as the Gold Coast neighborhood.
By car: from the airport, follow Ohio 237 north; from most parts of Cleveland proper, take I-90 or Ohio 2 west and follow the signs. RTA bus #26 serves both Lakewood and Cleveland along Detroit Avenue, and the Red Line features two stops just inside the Lakewood/Cleveland border, West 117 and Triskett Road, from which one can easily walk to the southeastern neighborhoods of Lakewood.
The areas of Lakewood of most interest to a visitor, notably the downtown area, are very walkable and bike-friendly neighborhoods. If coming from Cleveland, the #26 bus runs relatively frequently down Detroit Avenue and takes about 45 minutes between downtown Lakewood and downtown Cleveland. Driving in and around Lakewood is fairly easy as well. Please note that the speed limits are 20 in school zones and 25 on most other streets, and are vigorously enforced. Parking is limited in and near the downtown area, though paid garages and metered parking are available almost everywhere.
Most parts of Lakewood are fairly safe, particularly compared to most parts of Cleveland proper. Any place/time that you see runners or walkers, which would be most of the city most of the time, is likely fine. Streets within 1/2 mile of the Cleveland border (West 117th) are best avoided at night. Occasional fights outside bars and clubs, particularly in that area, happen from time to time. Standard common sense applies: if you must walk at night, walk in a group, do not carry valuables or large amounts of cash, do not make eye contact with anyone, know your route, and walk assertively.
Lakewood is well known an economically, culturally and ethnically diverse community. Prejudice in any form is not appreciated, but treat other people the way you wish to be treated, regardless of any differences, and you should be fine.