Hiking is a great way to explore the areas around you and find out more about the history of our great nation and states. Most places that have hiking have great over looks of beautiful lakes, prairies, rivers and other neat geological formations. I find there is a lot of beauty to be seen and I always try to make a day of it with friends and family.
Finding a spot can be quite easy. I have a lot of friends that go hiking often, so I just ask them where a neat place is. State and National parks have websites you can visit to find new places as well if you do not have many people to ask. I recently visited http://outdoornebraska.ne.gov/parks/guides/parksearch/findpark.asp to see what parks were near me. Some state and national parks have facebook pages as well. Nebraska, for example, does and they keep you updated for any free days for families where you can learn archery, if they have fishing days where you can use equipment for free, group hikes, living history acts and other fun activities.
After finding the place you want to go, you should always plan out your day. Tell someone who is not going with you where you are going and times you are going and coming back in case of inclement weather or in case other emergencies arise. Always check the weather before the days you are planning on going and on the day you are going to make sure you are going to have good weather or are prepared if there is a chance of rain.
I make sure all people in the group have water with them. I carry a few nalgene bottles, which hold one liter(32 Ounces) of water and are darn near indestructible.(http://www.basspro.com/Nalgene-Everyday-Tritan-Wide-Mouth-Bottle-32-oz-/product/10207661/) where my brother prefers to have his camelbak which already has a hydration system installed into a day pack.
I make sure I have all the essentials in my personal day pack like a camera to keep my photo journal up to date, a rain poncho, compass and a first aid kit in case of an emergency. When I check into the park I make sure I get a map of the park so I know where the trails are. I usually drive around the park, with who ever is with me, till we find a trail that we both agree upon or one that looks good to both of us. You can also ask the ranger when you check in if there is an easy/medium/hard trail (depending on your level of comfort) that they would recommend for you. Make sure you read the map to see how many mile that particular trail is so that you are fully prepared with enough drinking water and food. Most of the time the trails on the map will have special look outs or features marked on the trail on the map to make it easy to find the best features of the park easily.
I like it when places have benches to sit and enjoy a snack or lunch. Most scenic outlooks have benches or picnic tables so you can enjoy your view longer. They don't always have grills however, so make sure you have something simple to eat just in case. The maps usually have symbols to tell you if they do, I prefer not to carry too much while hiking though.
I bring along sandwiches that do not need refrigerating so they do not spoil. I also bring along granola bars, chips, jerky, fruit or something else to snack on while walking. You may have to walk several miles to get to some wonderful views. I also keep a cooler in my car with things I can cook over a grill when I get back from the trails. Hiking makes me hungry!
Some parks have grills readily available near parking for trails some do not. I pack a small grill and extra propane with me just in case. It always feels good to to have a full belly on the way home!
I hope you get a lot of good pictures out there!