Ultra low noise power supply
You'll need a switcher to pump up the input voltage, and have it followed by a linear regulator, like Russell proposes. His TPS717xx, however, while having a high PSRR doesn't have a high output current (150mA). High current and high PSRR don't go together well on LDOs. Nevertheless, an LDO may be required, since the 2-4V input volatge suggests that you're powering from batteries, and then you don't want to lose too much power in regulators.
A solution for the PSRR may be to use 2 LDOs in cascade, so that the PSRRs add.
The LP3878-ADJ may be a good choice for your second stage; it's low-noise, can supply 800mA and has an adjustable output which can be set to 5V.
For the preceding stage you could use an LP38690-ADJ. The datasheet shows how you can improve ripple rejection at higher frequencies if you place a 100\$\mu\$F output cap. Caps between each stage (100\$\mu\$F + 10\$\mu\$F + 1\$\mu\$F) are a must, but \$\pi\$-filters are a better idea: caps + ferrite bead + caps. Those should suppress the higher frequencies generated by the switcher.  

edit (re your update)
Dave rightly has second thoughts on your using AA batteries, but it's even worse than he calculated. I estimate that you'll need 7V from the switcher to feed the cascaded LDOs, so 600mA @ 7V is 4.2W, at a conversion efficiency of 80% that's 5.25W from the batteries. Two AA cells deliver 3V, so that's 1.75A from the batteries! Not only won't they last long, they won't like it either. I suggest you use a LiPo cell, which delivers 3.7V with a boost regulator, or even two cells in series, giving 7.4V, and use just the LP3878-ADJ. (If you don't use a switcher you don't need the second LDO to suppress its ripple.)