As they say, Hollywood is a state of mind. Few of the studios themselves are in Hollywood proper I think youll find that a car is going to be essential.
The only exception will be Universal Studios. There is a Metro Red Line station right at the Hollywood and Highland complex where the Renaissance Hollywood Hotel is located (note: be sure to take a tour of the Kodak Theater while youre there). In fact, Universal City is the next northbound station. The station is near the corporate offices, but there is a tram that stops right across the street and will take you up to the park and City Walk. If youve bought a VIP tour, that entrance is very near the parks entrance as well.
Warner Brothers Studio is only a couple miles away (in the city of Burbank) and is very impractical to reach by Metrorail*. It will be about a ten to fifteen minute drive from your hotel be sure to get clear directions from the hotels front desk. This is my favorite tour because of the history, the size and the constant production on the Warner lot. They, along with Universal, have one of the last remaining big backlots around town. I think when people visit a studio they expect to see acres of sets and familiar locations. Only Universal and Warner can offer that these days. Youll be driven around in golf carts and there is a lot of walking to do but that means youll get to walk through actual sets and actual production areas of the studio.
NBC Studios is right next door to Warner Brothers. They offer a tour of their facilities, which are mostly geared towards television production. This is the studio where they film The Tonight Show and you can usually see people lined up front. Ive heard mixed things about the tour, mainly that its too short and really doesnt explain a lot.
The Walt Disney Studios is about a mile east of NBC. They do not offer tours, but the Animation Building, Walts Water Tower and the Team Disney Building (with the three story tall drawfs) are all visible if you drive around the complex.
I havent been on the other two tours you mentioned Sony Pictures and Paramount Studios since they restarted the tours following a shut-down due to 9/11. So unfortunately I cant really comment on what youll see. Both are located south of Hollywood.
Paramount Studios is located on an interesting stretch of Melrose Avenue only a few miles from your hotel, but again I think a car is the only reasonable way to get there. There are also many gates into the Paramount lot itself beside the one they always show in movies. Be sure to check which street you use for the tour. On thing to note that while Paramount is a huge studio, there have a very small backlot. Most of what youll see depends on what theyve built in their soundstages. An interesting bit, Paramount is right next door to the Hollywood Forever cemetery. This is where the famous from Old Hollywood (1920-1970) can be found.
Sony Pictures Studios is further south and towards the west from Paramount. This lot is actually the old MGM lot and is steeped in Hollywood history. I dont know how much they talk about the old days on the tour (Sony is all about marketing whats coming up next), and the old MGM backlot was sold off a long time again (its now tract homes). Again, what youll likely to see is whats currently on the soundstages.
20th Century Fox Studios is a bit north of Sony and adjacent to Beverley Hills. As far as I know they are not offering any tours of either the movie or television facilities Besides from the mile long line waiting to audition for American Idol, the only thing to see is the large office building used in the first Die Hard movie.
CBS Television City is a bit further north and east and is the other big studio that people think of when they think Hollywood. Unfortunately they no longer offer tours either, but you can get tickets for sitcoms and game shows being taped there (beware of The Price Is Right fans!). On the bright side, LAs Farmers Market is located right next door as well as The Grove, the flashy new themed retail development.
I hope this helps. Enjoy your trip to the States.
* -Public transportation around town is designed to first meet the needs of the politicians, and the occasional needs of the commuters. Visitors or anyone else is pretty much out of luck.