How can I attract more wildlife without pests?  

You want animals that eat pests I would imagine. So things like frogs, bats, snakes, birds, etc.

The easiest way to attract these types of animals is to provide shelter. Frogs need a body of water, bats need housing, snakes need brush, and birds need trees to nest in. You can attract the birds with seed, that is the easiest one. The rest will take time!

Want to add about birds - the cool idea is to build a feeder for them from the wood. It should be an interesting thing 

Just provide them a reason to enjoy your space. I think the easiest way would be to add a water source as mentioned. You can do a small pond with a solar filter and fountain. You would probably want to put a few small fish in it to start just to control insects but frogs will eventually show up. This will also attract birds and other wildlife. 

I love having animals around my home but certain beneficial ones can become pests. The family next-door got a pool last summer and now we have tree frogs all over and every night for the last 2 or so weeks, it sounds like a jungle outside!

Water and plants. Depending on what you want to attract, I would just see what attracts what you'd like. Water will get you just about anything though!

Attracting animals is pretty easy. Supply food, shelter, and water. Depending on what you would like to see, just research what they like. You have to check for specific species in your area.