Have you been to Bali before? I think with a 9 month old I would be inclined to travel somewhere I felt fairly confident about food/water safety and transportation options, so that would either be somewhere I knew well and had traveled before or somewhere I was staying mostly in a fairly developed area in a private accommodation (rented flat) or a resort. I haven't been to Indonesia, but I have lived in and traveled a lot around South Asia and my main concerns would just be knowing we were somewhere with safe water, so I'd ideally want somewhere with a water filter on the taps (this will be the case in big resorts and some flats, less so in the smaller budget guesthouses). You can always use bottled water, but that's more complicated when it comes to washing things like cups, bottles, plates or toothbrushing or keeping bath water out of the mouth.
The other main concern would be food safety, so making sure that wherever you are, the quality of the food (assuming you will be eating out and not cooking it yourself) would be safe for a 9 month old. In both cases, I've had really varied experiences and it's not always the nice restaurants or hotels that prove to be the safest, so sometimes it's just luck. I lived in India for a year and drank the tap water and ate street food from the street vendors in the slums outside my office and got sick once for about 4 days. I went back to travel and visit friends and mostly stayed in a hotel and was cautious about where I ate and spent most of those 2 weeks sick, except for a few days when I was in a very remote and basic guesthouse where I was eating fish caught from the local river, and then I felt fine! So I would just give some thought to how you'd manage food and water safety and especially if you've traveled there before, maybe you'll already have some sense of what's usually safe and what's not.
The only other thing I'd think about is transportation and how you'll travel. I don't know much about Bali, but I'm assuming most local transport is by tuk-tuk? For long car journeys/airport transfers, you could bring a car seat, but you wouldn't be able to use one in a tuk-tuk, and you'd each likely have a child on your lap and no seat belts for anyone. I would probably feel fine about this for a 3 year old, not sure about a 9 month old, so that might just be something to think about in terms of your comfort level. Definitely places like Bora Bora and the Maldives would probably be a bit easier, as most people tend to stick to the resort areas and touristy activities, so you'd likely be more just in a resort or going on excursions for the day, probably in a car, which would be a bit more like here. Hawaii obviously would be not different than here.
I think it's really what your comfort level is. Having traveled a lot in Asia, I think I would be inclined to stick to something fairly easy with a baby in tow, probably just going to a big resort with day trips other places, rather than doing much traveling around or staying in more local accommodation unless you know the area well. And save the more adventurous stuff for when they're older and can appreciate the fun of it a bit more. It also depends on how nervous about things you are. If you are going to spend the whole time worrying about mosquito bites or if a certain restaurant is safe and you won't be able to relax and enjoy yourself, I'd do something more conventional. But if you are pretty relaxed about those things, then you might not find it's a big deal.