I recently acquired a 1988 Cannondale SR500, it's a very nice bike, but I noticed looking at it, how close the front of the rear wheel is too the seat tube. My Schwinn Traveler seems to have a more relaxed riding stance as I see more room between the rear wheel and the seat tube.

I have been looking at pictures of a lot of other bicycles here and noticed it's not unusual for such a close spacing, so I am assuming this is more of a sport bike built frame as opposed to a touring frame.

It rides very nice, quiet, sharp handling and all,

I need pictures to post,,,

Is there a question in there? I can't tell.

Anyway, probably what you're looking at with the Cannondale is short chain stays. Probably in the area of 405 mm. Racing bikes very commonly have that sort of dimension and a 25c tire gets real close to the seat tube and really, really close to the front derailleur clamp if there is one there. If you're looking for more clearance, you'll need to find a bike with a 410+ chain stay. They will also tend to be on longer wheel base bikes with other geometry differences (fork rake, angles, etc.).

You will also notice on a bike designed for racing that the steeper angle on the headtube will position the front tire much closer to the downtube than a bike desigend for more relaxed touring

how close is your rear tire?

Tight rear triangles were all the rage in the 70's in Southern California, I had a bike that I could not run a Del Mundo on, too close. That bike had its place, with its high Bottom Bracket and 165 mm cranks provided the ability to sprint to victory out of the last corner while others scraped their pedal. Not my 100 mile day ride though.

Later, I found I could still win without the think about riding all the time handling.