At 1.8 miles, you'll reach what is probably the most popular site of the hike, Punchbowl Falls:
Just past a little past that, there's a decent campsite where I would recommend settling down for Night One. Campfires are reportedly "strongly discouraged", but allowed, which is definitely a perk. If you do plan on making a fire, I'd recommend having plenty of starter fluid and paper on hand, as fuels may be moist.
If you are really adventurous, in the morning, you could continue for an additional 7 miles to camp at Wahtum lake:
Wow! Looks idyllic!
Hoofing it all the way to Wahtum Lake would make for a round-trip exceeding 30 miles, however, so it would need to be a full weekend trip. I have yet to make it past Tunnel Falls, so if you are planning on going, please invite me!
(Click for full size)
FYI: Parking is $5 per car, per day.
For more information on Eagle Creek, including history and directions, visit: http://web.oregon.com/hiking/eaglecreek.cfm
Sources: web.oregon.com; portlandhikersfieldguide.org