Phoebe:   Thank you for contacting the UVM Extension Master Gardener Helpline, asking about ground cover plant suggestions for replacing your lawn.  

Below, you will find links to information from other university Extension sites (with similar climates as ours) for your review.

Depending on your soil and site conditions, you may want to try creeping thyme.  Thyme is heat tolerant and requires well-drained soil (not an option if the area is wet with clay soil).  

Although, not native, Dutch clover is a good ground cover recommended for pollinator lawns.  Not suitable for very shady areas.  (See fact sheet from the University of Minnesota, below.)

Groundcovers for New Hampshire [fact sheet] | Extension

Planting and maintaining a bee lawn | UMN Extension

Dutch white clover | UMN Extension

Other native woody ground covers and low shrubs include:

• Arctostaphylos uva-ursi or bearberry
• Cornus canadensis or bunchberry
• Empetrum nigrum or crowberry
• Epigaea repens or trailing arbutus
• Gaultheria procumbens or checkerberry
• Juniperus communis or common juniper
• Vaccinium angustifolium var laevifolium or lowbush blueberry
• Vaccinium vitis-ideaa or lingonberry

This Plant Native link has a listing of ground covers, but you have to scroll down quite a way.  It allows you to click on each item for photos and more information.

Native Plant List for New Hampshire, Maine and - %sit...

The Cornell link below (Weed Suppressive Groundcovers) lists several groundcovers to consider when looking to replace your lawn.

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The next fact sheet from the University of New Hampshire discusses establishing a wildflower meadow.  This may be an option for part of your lawn, if you wish to do so.  In any event, the article explains ways of preparing the area for planting and describes the process of solarization as one way to remove the existing grass from the area.  

Planting for Pollinators: Establishing a Wildflower Meadow from Seed [fact sheet] | Extension

Below is a listing of sources for buying Vermont native plants.

Item - Vermont Native Plant Sources - figshare - Figshare

Finally, I would recommend having a soil test performed before planting, especially, since this is a new home purchase for you.  The test results will give you the soil PH, organic matter content, and nutrient content, to let you know if any soil amendments are needed.  Information from the UVM Soil Testing Lab is below, along with instructions on how to take a soil sample.

Agricultural and Environmental Testing Lab | University of Vermont Extension | The University of Vermont

I hope you find this information helpful.  Congratulation on your new house purchase and have fun making the yard your own!