"I go out to the hospital every week."
It is not normal Japanese to "dekakeru" to the hospital. Dekakeru is usually used for fun activities. Normally this sentence would be expressed using the regular word for to go, "iku", not dekakeru. One might say one "dekakeru" from the hospital, because leaving it, you are actually going out of it, but one would not normally go out to a hospital. Dekakeru would be going out with friends to have some fun
I really don't like exercices asking to translate new words first in Japanese. As mouse over the words does not work correctly, how are we suppose to guess that "to go out" is 出かけます ?
It looks like it was fixed. When I mouse over 出かけます it says "go out" properly.