You've reached the stage where you recognize that you can improve your photography, and you're wondering how to go about it. This is an exciting place to be, but also one fraught with confusion. The mistake that a lot of new SLR photographers make is to think that an ultra-sharp lens will, somehow, magically improve their photography and make their pictures look 'professional'. Actually, this is the wrong way to approach things. May I suggest that what you should do right now is think about how you can change your approach to how you take pictures? How can you make your pictures different from the crowd? Can you look at things in a different way? As a so-called professional, this is the question that I ask myself every day on the drive in to work.
L lenses won't inherently give you this - what they will give you is a robust and reliable tool that you can use every day without having to worry about it and that you can realistically expect will still be earning you money in three years time. Most of all, what you're going to get from an L lens is robustness, reliability, solidity and a tool that will do the job in adverse conditions, amidst a scrum of other photographers when, quite frankly, all you want to do is go home. Sharpness and color rendition comes a long second to all this. An L lens is just a working tool. Yes, generally, they will be slightly better than consumer lenses in sharpness terms (though not always), but there is a limit to this. It's not that L lenses are bad, more that these days, consumer lenses are really good, and good value to boot. Just not reliable or tough enough for day-in, day-out professional use. That's what you're paying for. Believe me, I'm much more concerned that my lens/camera will stand up to a bash against a wall than how sharp the lens is. When I want to make a memorable photograph, sharpness is a very minor consideration. Composition, perspective, content and subject interest and dynamics are what I'm looking for. I take accurate focus and an acceptably sharp result for granted, and even focus is a tool in itself. And you're probably going to be looking at most of your pics on a computer screen at best. Come on, guys, how many of you regularly print photos to 20x30?
So you want to spend some money. That's fine. First of all, go and get yourself a copy of Adobe Lightroom and learn how to use it. This will make more difference to your photographs than any lens ever will. Check out Lyndadotcom - it's a great educational resource. Learn how to use your camera in aperture priority mode and in full manual. Then, as JDRamirez suggests, get yourself a good prime lens and a polarizing filter. The new Sigma 35mm is a very good place to start. If I only had one lens, it would be a 35 prime (and my second would be a 135L). This will teach you to make yourself think before you release the shutter. It'll stop you being lazy and make you more aware than you believed possible of what's in front of you. Put your zoom lens away for a month or two and dream up some projects with specific themes that you'll use your new lens exclusively for. Rust. Specific colors. Water. Close up. Monochrome. Motion blur - whatever - anything that your imagination can come up with, but be strict with your self and don't goof off, because at the end of the day, the only person you'll be fooling will be yourself. Walk out of the door with a purpose and don't get side-tracked. Down the line, you can pick up a 300L f/4 or 400L f/5.6 or similar for your wildlife, etc. Same theory as the 35. For travel, you've already got a great lens. Personally, I'm not a great fan of ultra-wides (e.g. 10-22) until you've got a lot more mileage under your belt. They're novelty lenses in most people's hands, although that particular lens is very good on a crop camera. Whilst the 70-200 f/2.8 v2 is a magical lens on full frame, somehow, as someone else mentioned, it doesn't really gel on a crop body. Furthermore, you've already covered its range. If you really have to get a zoom, the 70-300L will work better for you.
Not sure that this is what you wanted to hear, but I remember when I had the same questions as you (back in 1978). I wish I knew then what I know now...
Don't know if you helped the OP's but you sure made me think
I'm gonna print this out!
Thank you for taking the time