Shelters for homeless veterans - they take stuff from me all the time - it's where I always take leftovers after a community event
Food pantries
Fire/police - we do it all the time in our town. The last people worried about being poisoned are law enforcement! Also consider state police if there's a barracks near you, because they don't have the local town resident loyalty.
Check with police domestic violence officers - maybe they can take your baked goods to a shelter for abused women. You can't - they won't give out the addresses, but maybe there is an umbrella organization that will take them on your behalf.
Senior citizen centers - holiday luncheons
Soup kitchens
No hospitals - they won't accept, and they have their own kitchen - and they have enough food. Go for the needy who need you more.
Nursing homes - may be a question for the reasons you mention. There are other things they need more, but check for individual requirements.
Groups that cater to new immigrants and new Americans - for example, we have a Latino service center which has a food pantry, a furniture/housewares "pantry" and a clothing/children's items "pantry". With all the anti-immigrant fervor, they need you more than ever. They will often do community meals and would be happy to have desserts.
Teacher appreciation at your local school? Especially the middle and high schools, where parents aren't as involved on a daily basis and kids have entire teams of teachers.
Make a little package for your letter carrier, your garbage collection guy, your newspaper delivery person, the attendant at the town dump/recycling center, and your FedEx/UPS drivers. These people are out in all kinds of weather and many are delivering heavy loads at this time of year. So many people fail to tip them, and a little homemade stuff plus even a small cash gift would go a long way!
Nice of you to do things for others!!