Here are a couple of different common paths you could go that are sub-$1000. But as everyone is telling you, usage is the easiest way to narrow down your choices to something you actually need, rather than something you just want. The easiest way to really start considering an "upgrade" from the kit lens is to consider in what ways the kit lens frustrates you the most. Then concentrate on those. If the kit lens isn't frustrating you, maybe it's not time to upgrade/expand.
Also, as a cautionary tale, from TOP, see Mike Johnston's "Letter to George".
I want it all, but I'm a tightwad
The most common path most folks will take to after getting an 18-55 kit lens, looking at the pics, and deciding it's gotta be the lens, not them is to finish rounding out the "training wheels triple"--that is, adding a cheap telephoto zoom and a cheap fast prime, most typically the EF 75-300 f/4-5.6 III (although the EF-S 55-250 f/4-5.6 IS is probably a better newer choice if a bit more expensive), and the EF 50mm f/1.8 STM (although the EF 40mm f/2.8 STM is wider and more compact and may be a better fit for general walkaround use, if more expensive and slower).
This will give you zoom vs. prime, fast vs. slow, and stabilized vs. unstabilized as a decision basis platform for later, and will cost altogether (assuming you got the 18-55 kitted with the body) less than one good mid-grade lens. And you're completely likely to want to replace all of these lenses later. But you need experience with lenses first before you can decide.
Try before I buy
Have you considered renting? Just to get a feel--widen the experience for your purchasing base. Find out if it's for you, or not your cup of tea. Maybe part of that $1000 budget can go for a $40/day rental of the lens you think you have to have.
I just want a better walkaround zoom
Some folks will go to superzooms for more reach (EF-S 18-135 or EF-S 18-200), or look at upgrading to a higher-quality/faster zoom of around the same range (EF-S 15-85 IS USM, EF-S 17-55/2.8, EF 24-70/2.8, EF 24-105 f/4L IS USM). The Ls are better-suited for full frame and are likely to be more than your $1k budget, while the EF-S lenses might be a better fit. But consider that what you're doing is looking at the lone hammer in your toolbox, and deciding you need to upgrade that hammer, without considering whether what you're really yearning for is a screwdriver, wrench, or drill.
But I really want to...
So. Maybe you don't need another walkaround zoom. Maybe you need a telephoto zoom to shoot wildlife or sports. Maybe you need a fast prime for blurry backgrounds and peoples' faces. Maybe you need a macro lens to get closer. Maybe you need a tilt-shift to make buildings absolutely straight or look like tiny toys. Maybe you need a fisheye lens to get in a ginormous distorted field of view. Maybe you need an ultrawide to get a really big view of things without curved lines.
My second lens was a fisheye (I'm really weird). I bought a dSLR to learn to shoot 360x180 panos handheld with a fisheye. It's what I needed. You are not me. You are also not any of the folks who are going to be handing you lens advice, based upon what they needed and like. dSLR lenses tend to work best as special-purpose lenses, not as general-purpose ones. What do you need to fill your toolbox with? Plumbers, carpenters, and electricians all carry toolboxes, but put different things in them. Tools for the task. What do you need? There's really no shortcut around the usage issue.
I'm a speed demon
Well, if you want to go fast and thin DoF with zooms, then get a bigger budget. f/2.8 zooms don't come cheap. And the autofocus issues with a fast lens in 3rd party makes may not be what you're hoping for when the pricetag is under $1000.
So, primes might be the path for you to walk, but then it's a matter of what length, what price. Do I go for the 28/1.8, the Sigma 30/1.4, the 50/1.4, the 85/1.8, 100/2, 85/1.2L, etc. etc. Easiest thing to do here is to look at your zoom lens usage, and see where you park your butt focal-length wise with a tool like ExposurePlot or the EXIF data in Lightroom.
But you may find that carting three primes about to do the work of one zoom might be more of a PITA than you thought, despite all that mystique on "zooming with your feet" and how HCB only used a 50mm, etc. etc. might make you think.
Maybe it's not glass I need
Maybe your $1000 is better spent not on glass, but on lighting gear. If your main focus is on portrait photography, getting a flash and learning how to use it--particularly off-camera in studio-style lighting setups--could be far more transformative than any single lens to your photography. And the cost of a good flash is roughly the same as that of a good lens.
You may also want to consider at this point if it's a tripod you need. Ditto whether shooting JPEG with Picasa/iPhoto at the end of the trail is what you want to be doing vs. shooting RAW and using the GIMP, RAWTherapee, Photoshop, Lightroom, etc. etc.
There's more to gear than just bodies and glass. Tools for the task.
Damn. It really is me, not the gear.
Maybe you finally took the time to google about to see what other more skilled hands can do with an 18-55 kit lens. Maybe it's not the glass. Maybe it's your lack of knowledge and technique. Maybe spending a little of that $1000 on a class, a book, video, or workshop is going to improve your photography more than any single piece of gear.
Maybe you just need to shoot 10,000 more frames before looking for your next lens.