Hello and welcome to the RTA forums !
This is a very popular area and discussed a lot throughout the forums so taking a look around will help get you started, the links in this thread contain some of our favorites.
The Heli tours from Vegas mainly go to the West rim of the Grand canyon on Indian lands and home to the "Skywalk". Whereas a helicopter ride is a great experience, you can't beat visiting the National park area by road, and witnessing the views and a sunset IMO. This is more than a day trip though and you would have to include an overnight stop in, or near to the park. The best of both worlds could be had by driving to the South rim and taking a 50 min flight over the canyon from Grand canyon airport in Tusayan.
Some people like the City life, others like me not so much, LA is huge and can take a lot of time to get around. Being from the UK myself, I prefer spending my time exploring the incredible natural wonders, such as Yosemite, Sequoia, Death valley, and of course the Grand canyon NP's. San Francisco is a great little City though, and one that I enjoyed a lot, plus between SF and LA you have the scenic coast drive around Big Sur etc.
There are so many Hotel rooms in Vegas they are constantly trying to fill them [and succed at times] and that leads to competition for the customers dollars. There is stuff to do in Vegas during the day but it really comes alive at night, if you wanted to leave town here is a great link to some day trips, and you can find out what the the locals get up to.
I would look at the links provided, work out how you want to spend your time with the help of a good map and then we will be able to help you with the details, enjoy the planning !