Yes Clearwater is close to Orlando. At least in my opinion. From Orlando International Airport it is 96 miles from the Orlando Airport and about two hours on average. It is after all on the west side of Tampa International Airport. Clearwater Beach FL is on a barrier island and Florida's Gulf Coast.
I am a hard core fan of Clearwater Beach and Clearwater Florida. These are the best beaches and beach towns in Central Florida. However, if you are just wanting a trip to the beach and not necessarily the whitest beautiful beaches then consider these.
Cocoa Beach is about an hour taking the most direct route from much of Orlando and Orlando International Airport. Daytona Beach may be closer depending on traffic conditions from downtown Orlando. The driving distance is far less and the beaches are plenty nice. The beach towns are inferior in my opinion to St Petersburg FL and Clearwater Florida. Both are still more suitable for day trips if you are visiting Walt Disney World or Universal Studios.
Amtrak to Clearwater Beach is just unrealistic. From Orlando to Tampa is only $17 usually but from there you need to get and Uber or bust to Clearwater. There is a train path to Clearwater Beach but it takes all day.
This can be done. However then you will need to get to and from the bus stations or take the risk of leaving your car at one. It is economical but so is parking in Clearwater Beach. As you might can tell I am encouraging you to drive from Orlando to Clearwater and besides there are some interesting stops along the way. Plant City is just one of which worth stopping by as it is right off Interstate 4.