My zoom pics always look washed out and blurry.
User error or a crap lens (it was cheap, 55-200mm nikon, cheapest one they do paid $150).

This is about the best I can get from it
http://lh5.ggpht.com/_ZV_KKwcwvOY/TC16us1FjhI/AAAAAAAArhA/J2YW9Oy30q8/s912/DSC_1041.JPG

If I need a new lens. Any tips for up to $300 odd ?

This is my current zoom lens

http://www.amazon.com/Nikon-55-200mm-VR-Vibration-Reduction/dp/B000O161X0/ref=pd_cp_p_1

Not uncommon for a long lens to be softer at the longest end but that does look poor.

Have you tried shooting at 200mm at a static subject from a tripod just to take handshake/subject movement out of the equation as far as softness goes.

Other possibility is camera settings - what settings are you shooting at? Higher f number might help with focusing.