If you are a W-2 employee. The decision to pay for the trip, and how it impacts their expenses and taxes is a decision for your employer. If your employer wants to pay for you to visit one of their offices, or to participate in an event or meet their customers, then that would seem to be a reasonable expense for them.
If you are a person with 1099 income. Then some of your expenses might be considered a business expense. Meeting customers is normal. Meeting potential clients is normal.
There are some complications:
However, it's a trip I'm paying for myself and I will do stuff that's
fun and maybe meet family members or something as well.
If you do work things during the day, but visit fiends and family at night that is fine. Once the friends and family start to be the focus the IRS considers it a vacation with very little work done.
I also received a personal development grant (from a program, not an
employer) and will use part of it to pay for the trip.
Now this makes it complex. If you have to send them receipts for specific items (airfare, hotel, ticket to the networking event) then those expenses are not deductible because they are covered directly by the grant.
If they give you $x and you can use it for anything then that $x is income. If you are allowed to count this trip as a business expense then those expenses will reduce the tax impact of the grant.
Talk to your tax advisor regarding these issues and the impact of your plan.