I know of four crossings between Kyrgyzstan And Kaz. The nearest to Biskek it's called Corday. Do ask for the right paperwork regarding customs. I crossed several times in the space of a year and only the first time they requested I filled a customs decalration (and that was at teh Kaz border with Russia, near Ashtrakan). I got into a fair ammount of trouble because I didn't have the customs decalaration and they told me they considered the bike in the country since the first entry.
There is another border not far from Corday that you will find on a turn right mid way on the road from Yssyk Kul to Bishkek. I don't know the name or have deatails about how to find it. From Kazakstan its easier to find, Just as you arrive at Corday, the Village --not the border--, before the bit with all the currency exchange offices you'll find it on a left turn. The road follows a river to the border and it's a much nicer ride but it will put you on the way to Yssyk Kul. The last bits had to tarmac two years ago and it may only be opened during the summer. I followed Kazak tourist buses there.
The other crossing its NE of Yssyk Kul on a road that goes round the Ala Tai. Again, a lot more interesting a ride.Also, about 200-250km from almaty there is a small turquoise lake called Bartagoy. From there you can climb up the mountains and ride about 200k over them, off road, and join the road about 50km from almaty. Spectacular.
Good luck there.