I began teaching Statistics with the same difficulty that you had. I started with basic sorts of questions (e.g., age, height) but my students weren't really responding to these types of questions. I sought to find a way to have them feel more connected to the data.
I began with questions about text messaging. (1) How many different people did you text on Sunday? How many total texts did you send on Sunday? These actually led to other interesting questions that we had to have as a class. Do we include group texts? Do we include picture texts? These types of questions that lead to the the exact discussions that you want to have with your students about data collection.
As this line of questioning developed, I started to have my students survey their own friends and contacts about their texting habits. This leads to other interesting data collection questions that we could discuss as a class. While we were able to get numbers we could work with, we had to be especially careful about what our population was, and how our data collection methods might not have been ideal. My last lab asked them about their flossing habits and total cavities. This didn't really provide the wide variety of data that I was hoping for, but it was suitable for my purposes.
The best thing about all of this what it opened up my students to start thinking about their own questions. They came up with many more questions than I could have. How many days a week do you work out? was a popular question. Shopping habits (online vs. in stores), coffee consumption (Starbucks or Dunkin), and QBR ratings for quarterbacks were all places that students pulled data from. I even had one student track her daily coffee consumption and sleeping habits for a month to use as a data source.
I'm not sure what level of student that you have, but for my college students of traditional age, once I was able to ask some questions about what they actually did in their lives (i.e., texting) it opened them up to the possibility of what other aspects of their lives Statistics could answer. I think if you can do this, then you'll help them to not only learn Statistics, but to teach them how they can use Statistics in their everyday lives.
I utilized a lot about their phone habits when I taught statistics recently. Number of total texts sent in one day, number of unique recipients of texts you sent, number of Instagram messages, etc. I can provide more details in an edited answer when I'm back on my computer