The minimum orbital inclination you can directly launch into (without performing an energy wasting "dog leg") is equal to the launch site's latitude. That's why launches from the Cape go into 28.5 degree inclination orbits if the launch azimuth is directly to the East. Tyuratam is at 45.6 degrees North latitude. They normally launch into a roughly 51 degree inclination because they have some clearance issues with China. That's why the ISS inclination was set at 51.6 degrees - so the Russians could launch their Proton and Soyuz boosters to the ISS.

You can launch into an ISS orbit from the Cape without too much trouble. The equation for calculating the orbital inclination is a simple one based on the launch site's latitude and the launch azimuth.

inclination = arccos(cos(latitude) * sin(azimuth))

To reach the minimum inclination from any given launch site, simply launch with an azimuth of 90 degrees. For the Shuttle to reach the ISS's 51.6 degree inclination, it needs to launch with an azimuth of 44.975 degrees. There is a payload penalty for going to the ISS but I suspect part of that is due to the energy needed to reach the ISS's orbital altitude of about 240 miles. The higher the Shuttle flies, the less payload it can carry.

A Proton or Soyuz booster launched from nearer to the equator than Tyuratam would benefit from the Earth's rotation being faster at the lower latitude. It'd be interesting to run the numbers to see if there's any performance penalty but off hand, I don't think so.