I do find situations when wider would be good, but overall not an issue.
Then you don't 'need' another lens, do you?
OK, D3200 & 18-55.
I have the same, plus the kit 55-300, which I seldom used, and rarely at the longer end, and for 'general' & urban work, I really wouldn't recommend.
On the wide-side.. have the sigma 8-16 UWA.. I think that the 10-20 is probably the more 'useful' UWA, though, things get a little fishy at the extremity of the wide-side; but all UWA's are a bit awkward to get to grips with, and if you aren't struggling to get things in frame with the kit? You really don't need it & one would be making more problem than it solved for you.
Now, the Kit 18-55 is not a bad lens, and for what it's designed for... entry level consumer camera's, its pretty astounding value for money... Cameras that come with them are often cheaper with them, than body only, so to my mind its actually better than 'free', they are giving you discount on the camera to have it! and you don't get much better VFM than that, do you! And for most in that market folk, it is a lens that covers the most used range of focal lengths, is acceptably 'fast' on apertures, and more than adequate for resolution.... BUT.... I think that the D3200's 24Mpix sensor started to show up it's short-comings, and probably the 55-3000's too. I get far better results with my old 'Legacy' M42 prime lenses on an adaptor than either, but they are a pita to use, with no metering, and no AF etc.
Now, I bought both the AF-S 35 AF-S 50 prime's for my daughter's D3100 and her school photography. Both retail for about £150 and compared to the kit zooms, are in a different league, and they atch the camera and still allow full functionality.
The 35mm is slap in the middle of the kit 18-55's framing range, and the 'normal' angle for a crop sensor body. Its a very versatile focal length, and without 'zoom' t will beg a bt more thoughtfulness from your framing to get what you want, rather than what the lens can gve you, while lack of zoom is one less distraction, so its a great training lens to apply more discipline & thought to your photography, while it offers better clarity and resolution, and the advantage of that fatastic f1.8 fastest aperture for shallow DoF effects.. it even has a focus scale, if you want to step beyond that and try exploitng selectve focus effects.. though lacks the old DoF brackts I like on my old screw-fit primes for that technique.
IF you aren't struggling with framing with what you got, for well under budget, off the shelf, or half budget 2nd hand, it would be my top recommend
As direct replacement 'upgrade' for the Kit 18-55? I am currently in a quandary on that exact topic. 18-55 in my most used lens, but mostly just for convenience; and having busted the bank to get the 'range' of focal lengths I have with my old film cameras, in widgetal, I find myself kicking myself thinking "Yeah, there's over a thousand quids worth of glass in the camera' bag.... NOT getting me better pictures, while I use the mount plug that came with the camera! WHAT am I doing!" As such the well regarded Sigma 17-50 is currently favourite for this years major photographic capitol investment; at a tad under £300 retail, its a bit over your budget, new, but you might strike lucky 2nd hand. f2.8 isn't as fast as the prime's, but is usefully faster than the kit's, while grade makes up for the rest, to make it a worth 'upgrade' for GP lens. 17-70 is also a contender; same price, same f-no, little added reach at the long end for versatility, but apparently not as well regarded for optics 24-70, sacrifices a fair bit of useful of wide-side, for the same small extra bit of reach, but is twice the price for the much applauded optics it has..Keeping it Nikon, the f2.8 16-80, would seem to offer 'it all' ways round.. but at a price to make my eyes water, pushing £700... ALTHOUGH, that is £700's worth of glass I, and I suspect most, would get the value from using, rather than as I have, sat in the bag most of the time, waiting 'those occasions' when longer/wider/faster is really needed, justifying the investment. But that's 'My' short-list..... Tameron do a 17-50 that's close in most things t the sigma, while Tokina's seems to have been discontinued... but stepping 'up' from the free 18-55 kit, almost any of them are likely to offer a big 'wow' for the spend.. its just whether you get the most from it.
Then it's into the compromises; with lenses in the UWA range at the wide-end heading into the wide-end of the kit, or looking at added reach super-zooms, and lots of pro's and cons to consider, just what you think you'll get most for your money from.... With suggestion of 'urban' & 'Architectural' a 10-20 or 10-24, might offer the upgrade in optics as well as framing range to tip the choice that way, alternately, for Gen-Photo, I have more often found myself 'eeked' at the cross-over point of 55mm on the long end, swapping 'twixt lenses and always having the wrong one for what presents itself! Making a 24-70 seem a worth suggestion. 18-140 or 18-200 is super-zooms I have pondered quite long and hard, given use I have pt the electric picture maker to in the last four years.. and being honest with myself, probably the more useful option; as widgetal, to me, is mostly about 'convenience'.. but then it's not really an 'upgrade' optically.. which chucks the whole bag wide open again.
BUT, if you are generally not 'struggling' for framing with what-cha-got... well, if t ent broke dont fix it! You don't need another lens. If you WANT another lens, then I would strongly reccomend you ponder the fAF-S 35, f1.8, as a way to build your technique.. without blowing budget, and use experience to inform way forward... 35 can be sold on for good money, you need not loose much on it, if you decide you really want a 'better' kit-range zoom, or to shift the range up or down, either way later.