We have 3 nights scheduled to see Hollywood and Disney. Should we stay in one place to see all three, or in one area to see Hollywood and another to see Disney?

Where is the best area to stay in to see both/either.

Any recommendations for places to stay in the area for under $200 per night?

Thanks!

LA has horrendous traffic. I would highly recommend staying in one area to see Hollywood and another to see Disney.

Will you have a car is the first question.

Kids along? There is really not much to "see" in Hollywood, unless you are doing a day at Universal Studios, the Zoo or the Observatory. If you have a car, I would stay down near Anaheim, and do a day trip for Hollywood, Beverly Hills, the beaches etc. Preferably Sat or Sun when traffic is lighter.
Anaheim is over-roomed and you'll get a lot more for your money there most times of the year.

No kids. Just want to see the touristy things in Hollywood (walk of fame, hollywood sign, etc).

Since you don't have kids I'd do 1 night in Disney and 2 in Hollywood.
I believe I gave you some hotel suggestions on another post. All of those that I listed should fit your budget. I've stayed at all the Hotels I listed at least once and they were all great. Personally since the Roosevelt has changed I prefer to stay in West Hollywood.
The Candy Cane is the best place to stay at Disneyland, other than a Disney property, and those won't fit your budget.
If you just want to see the Walk of Fame and that kind of stuff than 1 night in Hollywood would be ok. If you want to check out The Strip, check out Beverly Hills, drive through the hills or out to the beach, than do 2. Hollywood is really a lot more than that corner on Hollywood Blvd., there is a lot to do in the surrounding area.

Btw, you don't have to go anywhere to see the Hollywood sign. Just look up and you'll see it.

I you want a Hollywood trip, I would include a studio tour and maybe a TV show taping. When we vacationed in Hollywood we stayed the Hollywood & Highland Renassiance hotel, walked around Hollywood, toured Warner Brothers studio, saw a taping of the Tonight Show. Also saw them filming a movie in front of Graumman's, "The Italian Job", drove up & down Sunset Strip, walked around the Beverly Hills Hotel, went to Santa Monica, saw some star homes, ate at Mel's Diner, Pink's, etc...to me these activities defined my idea of Hollywood.

We also did Disneyland on this trip and stayed at the Candy Cane Inn in Anaheim.

Good suggestions isabella. I love Pink's. Another fun stop is the Farmer's Market on Fairfax with lunch or dinner at Canter's . A martini at Musso and Franks and breakfast at Nate and Al are also must dos while in Hollywood. Nate and Al has the best eggs benedict anywhere.

We had dinner at Frank & Musso's...old Hollywood for sure! Both at Mel's Diner and Frank & Musso's we overhead "power meetings" between Hollywood types about movie/TV deals.
Fun to listen in on.

We also went up to Griffith Park and Observatory.