Anyone with a park ticket can see the nighttime shows - light projections mainly with some fireworks. I believe that since the Frozen area opened there are night shows in both parks, but I've not visited since it opened earlier this year.
Staying in one of Disney's own hotels has the perks of early access to the parks (when selected rides and character meets are available). Most of Disney's hotel rooms are for 4 people, so if you are a bigger family options to stay on site are limited unless you book 2 rooms. (Connecting rooms are usually provided, but not guaranteed).
Disney hotels can be booked as a package with park tickets (and meal plans if wanted). The park tickets bought this way are heavily discounted so are good value and include both arrival and departure day park tickets.
Disney's hotels are:
Disneyland Hotel 5*, right above the park gates. Princess themed and with Disney Princess appearances in the hotel.
Marvel 4*, next closest, about a 10 min walk through the Disney Village area. I believe there is an exclusive superhero meet at this hotel.
I haven't stayed at either of the above, but they have been recently refurbished and I've heard lots of good things about them.
Newport Bay 4*, but not at the level of Marvel. Last refurbished around 2014 I have seen things suggesting its tired in places. Its also huge, so it can take 10 minutes from your room to the doors. If you are taking a pushchair or wheelchair there is only one tiny lift between the backdoors and restaurants to the rest of the hotel which is a huge bottleneck.
Sequoia 3* (I haven't stayed here, I believe its currently being refurbished). Generally the cheapest hotel with a pool.
Newport and sequoia are similar distances from the park, around 15 mins walk. There is an option to take a shuttle bus from the train station.
Cheyenne is 3*, but no pool. I like this hotel, its a series of 2 story buildings, rather than one huge hotel. Its Cowboy themed and has Jessie and Woody from toy story as character meets here. This one also has the advantage of offering a double bed and 2 singles, where as all the others have 2 double beds in most rooms. Depending on which block your room is it should be around a 20 - 30 minute walk to the park or there is a shuttle bus to the train station.
Santa Fe is 2*, cheap and cheerful, Cars themed. No air con. Accommodation is in 2 and 3 story blocks.