Looks like there are 8 listings for rent in that area. Only one is a comp to yours, listed at $3700. The one listed at $2600 looks awful. One of the worst listings I've seen. Shows it's been on the market for almost a year. The one priced higher than yours, at $4700, shows being listed for over a year. I question if either of these are still available.
Comparing your listing to the $3700: Theirs looks newish, very well maintained (driveway the exception), probably newer windows, with a lush green grass and nice landscaping. Yours has multiple different brick colors, peeling paint, older looking windows, dead plants, a half dead lawn, a walkway that is broken and slightly uneven, and an entry pad that is sloping rather significantly. Your kitchen looks nicer and more updated, but you don't showcase it in the pictures. Their backyard says cozy, safe, and well maintained - a place I'd want to use. Yours says uneven, uncared for, dirty, and needs work - a place I'd avoid. Flat out, your place looks unloved. You took care of the inside and ignored the outside. Children play outside. Also, your room pictures make every room look small. I don't know what it is, but every room picture makes me fell like I have to duck down.
Since the selling point of this place is the school district, you need to make your place child friendly. You need to clean up the place so it looks like a place people can envision living in with their children.
Front of house: Broken and uneven walkway and sloping entry pad says unsafe for my child. It's not a cheap fix, but it is a safety issue. Remove the dead plants. The multiple colors of bricks look awful. You can stain bricks to match. More ambitions would be to stucco it. At the very least I'd do the front of the house to make it look uniform.
Backyard: Looks dingy. Put the damn hose away before taking a picture. Clean up the yard. What is that old furniture in the picture? The fence looks super dirty in the last pic. Spend two hours power washing it and it goes from a dirty fence to fresh looking wood.
The paint is peeling some places outside. You don't have a lot of painted areas, so consider repainting the place.
Spend a few dollars on landscaping. Fix the lawn. Many people here will say not to do this as they'll just die. I feel landscaping can turn a house into a home. It can also help get the place rented faster.
Label your pictures. I have no idea what some of the rooms are.
As for price, if the other unit is truly a $3700 place and includes landscape maintenance, then yours is currently a $2900 place.
Fix the wording in your listing. If the school is the selling point, lead with that "Located in the Wilmette school district, this charming...". You have "no utilities included". Are utilities usually included? If not, remove this. Why are you offering a discount on first months rent is they sign before May 31st? You look desperate. Why are you offering a discount for a multi-year lease? Longer leases only lock the landlord into the contract. Renters can get out of the contract at any time. Consider bundling landscaping and snow removal into the lease. Two less things for a family to worry about.
I also wouldn't call your place a Cape Cod style home. Nothing about it says Cape Cod style to me.
And never forget, the market doesn't care what your mortgage payment it. No one will pay higher rent just because your mortgage payment is high. This unit may negative cash flow for a while.