After a quick search, I've settled on using Tick. I've been tinkering around with Tick for a couple days now, and I think it fits almost right into what I need.
Pros:
- Simple, easy to use
- Integrates with Basecamp
- Clear, simple reports
- Supports several users - track time of your whole team
- The non-free features, like Basecamp integration, are a bit pricey. 9$US a month is expensive for just a time-tracker. I'm not sure I'll keep with it after my free preview is finished for this reason.
- The Basecamp integration does not import milestones and to-do items, which are exactly the items I want to keep track time on.
- Adding new tasks to a project requires jumping through a few pages. It would be much better to be able to create tasks on the Time Card page.