So many different lights are available for under $5, you’d think that someone would put a better emitter in for a few dollars.
What is available in AA or AAA, that is WW or NW and under $10? Takes more than 1 AA or AAA is fine.
Finding warm white (3000k) in any stock AA light will be almost impossible. That’s what drive me to 18650s.
There was a group buy for the nichia edition of the sf-348 (blf-348). The current price at gearbest is $10.99 but according to GBGB: 4th batch of BLF-348 (Classy and Small 1xAAA Stainless Steel light, with Nichia NVSW219B-V1 R9050) - Coupon published! - #396 by _the you may still be in time to get a reduced price.
Simon also has a aaa light in his aliexpress store for $9.99. It is available in 4000K, 5000K and 6000K, at https://www.aliexpress.com/store/product/AAA-flashlight-EDC-flashlight-CREE-XPE2-led-inside/330416_32730506517.html
sub $10 there’s not much in AA available that I know of…
for a bit more, Jaxman E3 Nichia for about $23 at alieexpress, and L3 Illumination L10 Nichia for about $30 are a couple of decent AA prospects…
watching to see what other suggestions are put forth here…
The only option would be an emitter swap to warmwhite
Like XP-G2 R5-7A
Here’s another AA in NW for not too much $$ (still over $10 by a ways, though)
I just signed on to the group buy for the Utorch UT01 in NW here on BLF (search in the forums) at group buy price of $16.99 - it’s an AA tube light with a side electronic switch.
it SOUNDS like a good deal….
My best 1-AA tint light is a Bushnell TRKR T125L. I think they discontinued them at the end of 2015. I bought it mid 2015 IIRC, it was around $15 at walmart. It doesn’t advertise it but it has a great ~5000-5500K tint from the XPE2 emitter. I run it with a 14500 and it does about ~230L, its slightly brighter than my old Malkoff drop in which did 210L on the old CPF Sphere.
I also signed up for the Utorch UT01 in NW group buy. Seems like a good deal for $17.
I have an XPG3 - 5000k on order from ME with a 10mm board. Going to do an emitter upgrade on my old Quark 1AA. It has one of those yuky pale-teal-green XPG2 emitters. Long overdue for an upgrade.
For a single AAA light the ThruNite T01 is a really good keychain sized light , if you are wanting a small one with good output for such a tiny light.
They have those on sale for $6.95 right now on the ThruNite site.
http://www.thrunite.com/thrunite-t01-xp-g2-led-max-125-lumen/
My review on that light if you are interested is here………
Besides the BLF-348 mentioned above, the other 1xAAA that comes to mind is the Astrolux A01 - good Nichia neutral white, currently $8!
Another that comes to mind is this no-name stainless 1xAA XP-G R5 . Currently listed at $14.65, $13+ with BLF coupon. Not quite in your $10 limit, but noteworthy in that it’s actually a warm white LED coming stock in a budget 1xAA light. I picked up one of these after stumbling across it on the Banggood site, and I’m a little surprised I haven’t seen it mentioned here. The light itself is pretty well made, but the modes are mediocre - it’s L-M-H, but if I had to estimate the modes by percentage of final high brightness, it’s around 30-90-100… Not especially useful; basically a 2-mode light. The switch (tail clicky) is all metal and quite deeply recessed, so it wouldn’t come on accidentally in your pocket. If someone were so motivated to drop a better driver in this guy, it’d be a pretty nice light.
Finally, another with a pleasantly warm tint is the Thrunite Ti4 (I assume the slightly cheaper Ti5 has the same emitter). At $16-20, they’re definitely above your budget, but the tint is definitely in the warm range, even though they’re advertised as NW. The only reason the Ti4 isn’t my EDC pocket light is that the exposed switch is too easy to accidentally activate in my pocket. EDIT: As per the coupon code in this thread, some Thrunites at Amazon are currently 20% off, which puts the Ti5 closer to your $10 cap.
HTH!
Subscribing, as I’m always interested in new budget NW/WW lights! 
I just received the Utorch UT01 and like it a lot. Very bright with an Ultrafire 14500, although other 14500 protected and IMR supposedly don’t fit. I think they messed up though, one of the two I got is definitely a cool white when they were both supposed to be neutral white 3D.