Designation of Direction
When I want to mark a place that I left before came to somewhere, can I say "I came from..."? For example, "I came to Seattle from Los Angeles", meaning I left Los Angeles and came to Seattle. Or "I went home from a grocery store."

Question

Answer

Yes, using "from" like that is perfectly acceptable and normal.

Answer

All of this depends on where you are located when you make these statements. Your first sentence is perfect English if you are presently in Seattle (I came to Seattle from LA.). If you are not in Seattle when you say it, you would say, "I went from LA to Seattle." Your second sentence is possible, but only if you are at home when you say it! If you are not at home, you would say, "I went home from the grocery store."