Many love the Tamron and Sigma 17-50/2.8 kit.zoom replacements; these would be within your budget (I think) as would the DA16-45/4. The DA*16-50/2.8 would be better, but it's definitely a budget-buster.
Are other walkaround options. My basic lens is the DA18-250; my 240 others are specialty items. No, the DA18-250 isn't the fastest nor overall sharpest, but it's THERE. The IQ of a missed shot is zero. It's just the most flexible lens for travel.
For sharper and cheaper, consider something other than a one-size-fits-all solution. My favorite replacements for the DA18-55 are the Cosina-made Vivitar Series 1 19-35/3.5-4.5 (MF) and the SMC-F 35-70/3.5-4.5 (AF). The F35-70 is the smallest zoom Pentax ever made, is extremely agile (VERY fast AF), is sharp as a bag of primes, and is a bargain at around US$50. The Vivitar is very sharp, like many 2x zooms. Mine is MF, but AF Vivitar- and Cosina-badged versions can be found. I could maybe point you to a source of the Cosina version, selling price US$70 plus costly postage from Germany.
My basic most minimal AF kit: DA10-17 fisheye zoom; Tamron 10-24 ultrawide zoom; DA18-250 superzoom; FA50/1.4 Fast Fifty; Raynox DCR-250. All except the Tamron and Raynox are my original kit, and still most-used. To 'replace' the DA18-250 takes the 19-35 and 35-70 I mentioned, and the FA100-300/4.7-5.8 (silver), another VERY sharp bargain lens, around US$100.
Last edited by RioRico; 06-16-2012 at 02:47 PM.