http://datasheets.maximintegrated.com/en/ds/DS1337-DS1337C.pdfI suggest finding a TI-83+. It is essentially identical to the 84. The primary differences that might actually affect you are that the 84 supports mixed fractions (e.g. 8_1/3 instead of 25/3) which you should never use anyways, and it can be set at an OS level to always use fractions or decimals instead of being determined by the input. In terms of input, the 84 is curved, but otherwise the keypad is identical. The most significant differences between the two are that the 84 has a real time clock, more flash rom, and a faster processor. The 89 is my calculator of choice since it has a great deal of support for calculus (including some really complicated calculus) and even primitive support for abstract math (not much, but some), but it is a completely different best from the 84, so if that is what is being recommended, I don't think you will want to go that route. I wouldn't skimp too much on a calculator; depending on how far you want to go in math, physics, and to some extent chemistry (especially anything involving statistical mechanics), having a decent graphing calculator will save your ass more often than you can imagine. However, it sounds like an 83+ would be perfect for you, and you can find them used on amazon or ebay for like 40-50 bucks (I have seen them cheaper, but that is the cheapest I could find right now).
alphamule: I would love to see you program an RTC into an 83 XD
You can also fake it like they did on a lot of microcomputers from the 1980's. They just had the BIOS call to read the clock go to a counter that was incremented by an interrupt. As far as I remember, hardware real-time clocks still worked without a battery, but you had to keep setting the time. This actually was kind of required as the clock was directly tied into the keyboard controller on some machines? Oddball serial interface timings, hehe.
Hmm, come to think of it... I think I remember seeing some I2C or similar interfaces on a 8Mb+ Flash memory chip. Ah, found it. Too bad that the drivers don't exist on the TI-83, AFAIK. Oh, and you can't get the chip anymore, but the M25P32-VMP6TG is pretty similar in specs. In theory, any interface that works with the few pins of a link cable would work, or you could use a multiplexer/latch/buffer combo chip. Yeah, slowwwwwwwwww, but it works. Ugh, bringing back memories of the Commodore 64 drives and their hacks. No need to use some hard-to-find memory chip. If I was going to go this route, I'd just get a cheap microcontroller with built-in USB OTG and make it work with any FAT16 drive. In practice, probably best to have image files that represent a virtual drive in some calculator-friendly file system. The µC would be able to do much of the work, so an easier-to-implement (and port) driver could be used. The SPI's 4th pin can be tied to ground, and some kind of multiplexer be used (in practice, you'd use it in Microwire compatibility mode, but it's still not worth it when there's fast microcontrollers out there cheap.
http://hackaday.com/2006/09/14/usb-flash-drive-on-a-ti84/ Too bad this needs the USB port, but if they ever make one with a micro SD slot, you won't need to replace your TI-84 to get 1GB or more of storage space. Maybe they could call that one a TI-87 or better yet 'TI-Xpire' since it'll probably be the last line sold before they might as well make it a rugged 4" tablet. XD