Flight
Faro is probably the closest and cheapest option. There are buses or cars you can rent from the airport to Huelva. Please take into account that Faro is in Portugal and it takes about 1h30m to get to Huelva. Also take into account the time difference!
House Or Rental
We have people from church that will open their house for you to stay there. But places are limited, so please let us know if you're coming and how long you're staying so we can arrange a place for you. Booking.com also has good prices for hotels you can look at, you could also arrange to get an Aribnb with a few others coming from N.I. or you can let us know and we can help you find a place to stay.