I took a daytime tour at the Neon Museum earlier this year and really enjoyed it. Be aware that almost the entire hour long tour is outside with no shade. Heat can definitely be a factor in how much you enjoy it. I also don't recommend bringing small children as parts of the boneyard are roped off to keep everyone safe from sharp metal and broken glass. Kids almost instinctually want to explore those areas. Give yourself time to check out the gift shop in the visitor center (what was formally the lobby of the La Concha Motel).
As for discounts, regular daytime admission, for those over 18 is $18, but seniors, students, active military, veterans and Nevada residents get in for $12. At night the regular admission is $25 with seniors, students, active military, veterans and Nevada residents paying $22. If you don't qualify for any of the discounts, the best deal I found was the combo deal with the Mob Museum. Get tickets for both museums for $30, $37 if going to the Neon Museum after dark. That deal is offered at the Neon Museum website during the ticket purchase process (The Mob Museum site offers the deal then sends you to The Neon Museum via link to purchase the tickets). You have to reserve the day and time of your tour when you purchase the Neon Museum ticket as space is limited. You also have to use both tickets within 7 days of each other.