Which side you are on matters
Hurricane, La Verkin and Toquerville sit on the SR-9 corridor approaching the park from the west. Springdale is at the gate. Orderville and Glendale sit north of the east entrance in Long Valley, in Kane County. Those are different markets with different price structures and different traffic.
Seasonality is real
Park traffic is not evenly distributed through the year, and neither is life on the roads that serve it. If you are considering a property on a park approach, drive it in peak season before you decide.
Access and utilities
The closer you get to the park, the more variable services become. Ask specifically what reaches the parcel and who maintains the road.
It affects value in both directions
Proximity supports demand and it also brings traffic, seasonal crowds and short-term rental activity. Whether that is a benefit depends entirely on what you want from the property.