We went last year for 4 nights / 3 days and stayed at the lego hotel. The lego house was amazing, definitely plan to go, and allocate a day with lunch at the mini chef robot cafe.
We did 1 day in Legoland, 1 day at the lego house, and another day at Legoland (we got discount tickets for the 2nd day at the end of the first day) We went outside of Danish holidays so it was really quiet and we got on the rides with no queues. Highlight here of Legoland was the driving school, 4d movies and the ninjago arena. We went at opening to the lego house and stayed there til about 3pm
Billund is very walkable (can get to the town centre from Legoland in 10-15 mins) and there's some nice small cafes, bakery, restaurants and grocery stores etc
There's loads of lego shops, but it's very £££££!. If you keep receipts, you can claim back tax at the airport. The lego hotel is ok for the experience but it's dated - I know it's small things but there's no air con or heating in the rooms, room service was very hit and miss, not sufficient storage for clothes and empty bags (there were 3 of us with winter clothes tho, which might have contributed) However, the restaurant was decent for breakfast, staff were great, and there's loads of play areas for the kids, inside and out.