Where in Delaware? If you are in the Wilmington area there are really nice local opportunities for hiking, trail running, mountain biking, and canoeing within Brandywine Creek SP, Woodlawn Trustees land, and White Clay Creek SP. OF course there are no mountains, but more short up and down than you would expect. My favorites are the Adirondacks, which are more like a 7-hour drive but well worth the trip. There are lots of good possibilities in West Virginia and Virginia within a 5-hour radius.
Hey I just moved out of Delaware! Brandywine state park off of 141 in Wilmington is nice. Brandywine Creek Park is a shorter paved path mostly used for running but is nice. Alopocas is also a nice paved path. White Clay Creek park is nice, it is in Newark and runs into Penn. Fair Hill in Maryland is a nice park where they have some hiking trails off of 273 in Maryland. Bombay Hook is on the coast about halfway to Lewes from Wilmington, just outside of Smyrna, it has really great birdwatching. Other than that if you want real wilderness you need to leave the state. Pa, Md, Virginia, WV, NY, and of course the other Northeastern states have lots of opportunities as well. I visit the Adirondacks as much as possible.
Also forgot to mention there is a really nice top-roping area in Alapocas Run Park on the E side of the Brandywine Creek in Wilmington. It has about 80-100 ft. of vertical. It had been a mess, but volunteers and park personnel took a lot of effort to clean out the poison ivy, etc. and it is now a first rate climbing facility. The local parks are even offering beginning climbing classes!