A good rule of thumb: If it's outerwear meant to protect you from the elements, it's probably best to dry clean.
Anything valuable/formal should be dry cleaned.
But most semi-formal, business-type clothes, casual night out clothes, even if fancy in appearance can be machine washed with cold water, especially with newer more gentle washing machines & detergents.
The dryer is a different story and it's a good idea to just never dry anything on high heat at all ever unless you're literally trying to kill something (by disinfecting it lol). Even t-shirts last longer when dried on low heat.