If flying recreationally in the U.S. you are covered under FAA section 336 and there is no height restriction. I keep seeing people that think there is a 400ft restriction...that is only if flying commercially under Part 107.
Here it is right from the FAA Page:
Fly under the Special Rule for Model Aircraft
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To fly under the Special Rule for Model Aircraft you must:
Fly for hobby or recreation ONLY
Register your model aircraft
Fly within visual line-of-sight
Follow community-based safety guidelines and fly within the programming of a nationwide community-based organization
Fly a drone under 55 lbs. unless certified by a community-based organization
Never fly near other aircraft
Notify the airport and air traffic control tower prior to flying within 5 miles of an airport*
Never fly near emergency response efforts
For more information about what you can do with a model aircraft, please read FAA Advisory Circular 91-57A (PDF) or read the Interpretation of the Special Rule for Model Aircraft (PDF).
If you do not meet these requirements, you must fly under the FAA's small UAS Rule (part 107).
*The person flying the model aircraft is responsible for contacting the airport directly. Many phone numbers for airports are available here:
Airport Data
Many airports have processes for people who fly near their airport, and the model aircraft operator can talk with them directly about how to meet this rule.
Registration Requirements
The FAA requires you to register as a "modeler" and mark your model aircraft with your registration number in case it is lost or stolen.
Registration costs $5 and is valid for 3 years.
More information about the registration process is available through UAS Registration.
Additional Resources
Examples of UAS that do and do not require registration (PDF)
Frequently Asked Questions
Definition of terms in the Special Rule for Model Aircraft (PDF)