You're right to look within linear regulators if you want to get the best performance from analog chips ("digital" accelerometers/gyros are still analog at their core), SMPS almost always have much more ripple unless you're looking at really old linear regulators with tons of input ripple
Accuracy shouldn't matter (within part tolerances) as the sensors are generally ratiometric, though as always, check the datasheet.
You want low noise, but how you minimize that depends on the broader context. If this is battery powered there shouldn't be much input noise, so a general low-noise regulator would be best. However, if you also have other parts on the same voltage rail (e.g. a radio) that might switch on occasionally and eat tons of current, choosing one with good transient response might be better. If it's line driven, you may want better input rejection (if you have a terrible AC/DC supply).
The best performance you could squeeze out of them would be to put them (and other analog parts) on their own voltage supply where you would know that nothing would be switching in and out very fast, putting noise on the supply.
From my limited experience with some MEMS accelerometers five years ago, it's pretty easy to hit the noise limits of the device (though they've come way down in price and performance has probably gone up as well), so don't go overboard unless you know your supply is what ails you.
It looks like you misplaced the feedback resistors. They are tapping off the wrong end of the inductor.
Making a switched regulator on a breadboard is asking for trouble. If you check the manufacturers demo board layout you see that its nowhere near this type of breadboard layout. With this you will have stray capacitances, messy ground paths to mention some of the problems.
Best Answer
You need either a buck-boost switching regulator or a low-dropout regulator. The P-type output transistor of a LDO linear regulator gives a dropout measured in hundreds of millivolts versus a much higher dropout for linear regulators that use a N-type transistor instead. They are a bit more unstable though, so be sure to read the datasheet very carefully.