Here are some potential pros and cons of buying a property in the village of Eagle, Nebraska:

Pros:
- Peaceful and serene environment; living away from the hustle and bustle of the city
- A strong sense of community and a friendly neighborhood
- Lower costs of living in comparison to the city
- The opportunity to live closer to nature, and take advantage of outdoor recreation activities like fishing, hunting, and camping.

Cons:
- Limited access to urban amenities and entertainment options.
- Lack of public transportation options and limited connectivity to neighboring areas
- Reduced employment opportunities, mainly reliant on the agricultural industry
- Risk of natural disasters like flooding, tornadoes, among others, depending on the local geography.

It's important to visit the location and do some research before making a decision to buy a property. Also make sure to get professional help from a real estate agent or attorney to ensure a smooth and secure transaction.