Hiking Mount Whitney is an amazing but challenging experience. The hiking trail is about 22 miles round trip. You go on the same trail out and back so you have twice the opportunity to enjoy scenery while hiking. The hiking trail is near Lone Pine California. The hiking trail is typically most beautiful by my experience from March until November.
You can complete the hiking trail in one day. However expect about 12-13 hours of hiking to do the trail. You may want to spread it out over multiple days so you can enjoy the scenery more. Additionally the trail can be very hard since over half of the trail is rocky and requires a bit of scrambling.
When you go make sure to bring water. The winter time gets dry and summer is even dryer. Even if you have purification systems it can be tough to find want. The hiking trail can get stormy, especially in the winter. Plan ahead in case you get snowed in. At times you can even get to see some ice in Spring. If you want to enjoy it with minimal crowds try going on a weekday. On weekends, especially in the summer on Saturdays it can get very very very crowded. Also you need to get permits so on crowded days you may not have the chance to go hiking her if you try to get a permit tooo late.