Of course, "best" is relative, but West Little Rock is booming. All the neighborhoods of Chenal are newer and desirable. If you prefer older/historic homes, the Heights & Hillcrest are for you. They are bordering neighborhoods closer to downtown and have a "small town" feel. Leawood is in between both in age and in geography. North Little Rock is similar and the home prices are generally a bit lower there. Maumelle is also a consideration. It is a small town between Little Rock and N. Little Rock. It is entirely self-contained but also very convenient to WLR.
The weather is a bit crazy this time of year. Generally speaking, it is quite warm and humid during the summer and fairly mild winters with very little to no snow.
Please let me know if I can help you in any other way. I'd love to show you my home town!