Arranging temporary childcare during a conference in an unfamiliar city

The easy but expensive way is to ask your hotel. They will have reliable regulars available and will take care of finding somebody who can work with your schedule. While this is unlikely to be an issue in Utah, the hotel will also have babysitters on call who speak enough English to communicate with you and manage older kids as well. Obviously, you'll pay a hotel premium for the privilege though, but if the conference is paying, this shouldn't be a problem.

The other option is to find somebody on an Internet babysitting site like care.com (no affiliation). This will be cheaper, since the middleman takes a smaller cut, but you'll have to do your own research.

As an aside, though, I'm hoping your child has not developed separation anxiety yet, since this is common around the 1-year mark, and can make babysitting by a stranger difficult to impossible. I'd advise trying out getting a non-parent to babysit before you leave for the conference and are left with no other options.

Ask the conference organizers. They've thought about childcare enough to offer reimbursements so they've probably also thought about what options are available. Furthermore, the local organizers (i.e., the people organizing the venue, rather than the people organizing the academic programme) will be locals and there's a good chance they'll know about local childcare options.

You often can find childcare through sitter websites. The main two national sites are Care.com and Sittercity.com, though there are many others; search Google/etc. for "Babysitter" by itself and you will find the national ones and likely your local ones, if you include the city name you might find some local area ones.

The national ones will cost some money to register for, but will have references and some background checks built into the service. You also will see reviews by others who used the particular caregiver, which can be nice if you don't want to put in the work of thoroughly checking into someone's references.

Specific to Salt Lake City I'd be curious of two possible sources: the local Ski resort area, and the Mormon Church. We ski in Aspen and there are several dedicated services for that area to find childcare (As skiers often want someone to watch their child while they ski/drink/etc.). SLC (and very nearby Park City) seems to have the same, given that area is a major ski destination. Searching on Google I find a number of similar services; if you go local, I recommend a proper service rather than Craigslist, as you can have background checks done (either at your request, or many of the managed services will have already done them). Most of these services will come to your house/hotel/etc.

Secondly, the Mormon Church is very family oriented, and likely will have a lot of folks used to caring for children looking for short term jobs (both teenagers and older). You may be able to find some connection through there to find a recommendation. I don't have any specific knowledge, but I've known folks who were able to find childcare through other churches in other areas.