"I suggest that you ___" is a formal way to give someone advice. Because it's so formal, it doesn't sound friendly. In fact, people often use this phrase to express that they don't care about someone else's problems. For example:
A: I don't have any money.
B: Well, I suggest that you get a job.
In this example, Person B doesn't feel sympathy for Person A not having any money.
As another example, imagine an argument between a tough boss and her employee:
Boss: I need you to come in and work this weekend.
Employee: What? I had to work last weekend. I was supposed to have this weekend off.
Boss: I'm sorry, but I need you this weekend. If you don't like it, I suggest that you find somewhere else to work.