i'll catch it for recommending this but there is no doubt that if the weather is good the place with the best views is shooters on the west bank flats. just have beer or simple drinks and dont bother eating there.
also in the flats - the most "clevelandy" blues bar i can think of is hoopples:
otherwise, cleveland's classic remaining old blues bar is brothers:
the new owners revamped the place so i cant vouch for it's divey looks anymore, i'm sure its all buffed up now, but i just am glad to hear its open again.
lastly, thee classic cleveland rock bar dive is pats in the flats:
its an old man bar in the daytime, nighttime is another story!
again, other than pats these are anti-trendy, but basic classics of their type. have fun and report back!
The coolest spot to drink in Cleveland doesn't really meet some of your criteria - but if you want to truly sample the art of the cocktail in a refined, but fun setting - The Velvet Tango Room. The age of the crowd really ranges from 21 on up - but it is not a RR/Blues place - the nightly entertainment is focused more towards Jazz and standards. The TVs are set to TCM, and also to black and white. There is a delightful patio in the back, and the super-secret back room. Neat attire is requested. http://www.velvettangoroom.com/
You might check them out during happy hour (when drink prices are reduced) then continue on to more trendy, RNR kind of spots. I know we have them - but I can't tell you where!
Velvet Tango Room
2095 Columbus Rd, Cleveland, OH
I second the rec. for Velvet Tango room as the "coolest" place in town, but Prosperity, Happy Dog and Parkview are also good suggestions. Brothers Lounge in Lakewood would also be a top recommendation, as well as Mercury Lounge downtown and Lava Lounge in Tremont .
1392 W 6th St, Cleveland, OH
Prosperity Social Club
1109 Starkweather Ave, Cleveland, OH
5801 Detroit Ave, Cleveland, OH 44102
11607 Detroit Ave, Cleveland, OH 44102
1307 Auburn Ave, Cleveland, OH