That's a nice time to come with an 18 month old. You may be here in time for the Cherry Blossoms on Old Mission and Leelanau Peninsulas. The Children's Museum is definitely good. Your child may also like the Discovery Room at Dennos Museum. They have lots of interactive items like a harp with no cords that plays. You'll like it too! I still do! :)
There are tons of places to eat - many that are kid friendly. Jolly Pumpkin is very good - old mansion and the inside is very lumber-baronesque (it was once the home of a lumber baron). You will probably like North Peak Brewing Company, Mackinac Brewing Company, and Blue Tractor. All are downtown and great places with great food for adults and children. You may also like Travino Traverse Wine & Grille. It's a nice atmosphere with lots of selections (pasta, pork tenderloin, NY Strip, etc).
As for a place to stay, I run the Cherry Tree Inn & Suites. Without being too partial, please check out our website and our reviews on Tripadvisor.com. We offer great accommodations for families. Plus, we'll have our new outdoor pool near completion in May. We have an indoor pool and hot tub, free hot breakfast, guest library, HD TV's, and 24-hour Sweet Shoppe.
Hope this helps. Thank you for coming to Traverse City!