Many micro-recorders, like the Zoom H2, don't allow overdubbing.
If I wanted a field recorder with overdubbing and built-in mics, I would consider a "portastudio" like the Zoom R16 24-bit multi-track recorder ($399 for 8-track recording and 16 track playback). The Tascam DP- series are popular and some have built-in mics - check out
the DP-008 16-bit recorder ($215 for 2 track recording, 8 track playback).
If your heart is set on one of the micro recorders with overdubbing and internal mics, then +1 on the
Zoom H4n. It has 24 bit recording ($299 for 2 track recording, 4 track playback).
Slightly incorrect, The H4n can do true 4 track recording, as long as 2 of those inputs are either the onboard stereo mics or the 3.5mm stereo mic input. So- for instance, you could use the mic stand adaptor, putting the H4n over a set of drums, using the onboard mics as the overheads, and connect the kick and snare mics to the XLR inputs, and record on 4 tracks. Or- you could plug the output of a small preamp into a Y cable, and then into the 3.5mm input, and record 4 tracks with any blessed mics you want. It's a slight impedence mismatch, but I've done it and it works. You just have to turn the preamp way down.
Note that H4n does record in 24bit/96kHz, but only in stereo. The max bit depth/resolution in 4 track mode is 16bit/44.1kHz.
Bottom line- H4n does everything the OP wants, and more. Want cheap? Look around on ebay for an obsolete unit- Korg PXR4 Pandora. It has some limitations, but does everything the OP wants. You can find them real cheap now. Here's a rundown:
1. Only one onboard mic. For stereo recording, it needs an outboard stereo mic.
2. 16bit/44.1kHz is max resolution and bit depth. It can record in 2 lower formats as well.
3. It has a USB port, but doesn't export WAV. or MP3 files. It only puts out MP2 files, which are huge, and can then be ripped to MP3. But- you can't then process the tracks in a computer. It simply isn't a computer interface.
4. It has a 1/4" mic/instrument input for a dynamic mic, guitar, etc. No phantom power
5. Limited memory due to obsolete Smart Media cards. Max is 128mb, which in high resolution= about 90 track minutes, 45 minutes in stereo, 22.5 minutes in 4 track.
Check the I/O, and the limit becomes obvious. You can really only record 2 tracks simultaneously, no matter how you set it up. For what the original poster asked for, it should work just fine. BTW, the onboard effects on the Korg are amazing for what it is. The little bugger even has a drum machine in it.-Richie
PS- I just checked ebay and you can buy a PXR4 used with the 128mb card as a "buy it now" for $119.