I am in the process of applying to several graduate school, so I need to write several Statements of Purpose (SOP). English is not my first language and my writing skills are average at best. Are there any tools online that could help me improve my writing either by suggesting alternative words/phrase or correct my grammar? Ones I have found so far that looks good is Grammarly. Would you recommend the premium version or are there an alternative that works better?
If you use Grammarly, take it with a grain of salt. Software can be useful, but it is by no means a replacement for a human eye trained to read a language. Reviews of Grammarly tend to not be very favorable.
If you must use software, either Grammarly or LanguageTool will work.
You say you're applying to graduate school. Did you go to undergrad in an English-speaking school? If so, see if you have a writing center of some sort available to you. They will be able to go over your statement of purpose, and give it a more thorough critique.