Africa

Your first step should probably be to look at the US State Dept travel advisories. Only you can decide if you will feel safe.

https://travel.state.gov/content/travel/en/traveladvisories/traveladvisories.html

Is there a reason why you are worried? I think you can count that any established travel company that offers safaris has established procedures to protect customers from dangerous wildlife.

'Safe' is a personal state of mind. Sure, look at travel advisories, but sometimes people feel unsafe in unfamiliar surroundings. Then only you can decide. Of course, once there, you need to abide by the rules for safety from animals, but tours tend to keep you pretty close together and don't encourage independent wandering, so city time should be fine as well.
I will make this comment, as I have been to Tanzania several times, the worst to happen is petty theft. Remember anything we have is more than most have there, so don't leave money, valuables, or trinkets lying around in your room or tent. Either lock them in your suitcase or carry them to meals with you. Rooms are turned down during dinner, so keep that in mind. That is where I got in the habit of living out of my suitcase and leaving little to nothing on surfaces when away. Clothing hung up is fine. On the other hand, I left a small package of things for the cleaning staff but without a note, and I received an email asking where they could mail the items I left behind. Petty theft can happen anywhere there is access by staff, anywhere in the world, so it isn't necessarily worse in Africa.

We did a Safari with Twiga Tours, based in Nairobi. If you contact them with your concerns I think they will outline to you their measures to keep their clients and themselves safe. Safety from the animals is a given on any Safari, I should think. We were never allowed to get out of the vehicle for one thing.

Edit
We all did get out if the vehicle once when it got stuck in the mud and we all had to push it out. That was fun.

We were more concerned with the civil unrest and attacks in public. We are with the STEP Program

Have no idea what the STEP programme is, but I did understand that is it not safety from animals that concerns you.

Sara, these 2 countries are level 2 - like France and numerous other countries. If you do some checking, you will see many countries in Europe have been on high terrorism alert for a number of years. Terrorism in Kenya is near the Somali border. Kenya has, however, been undergoing a longer period of unrest due to politics and recent elections. Once out of Nairobi in on safari, you will feel like being in a little bubble of travelers and nature. Nairobi does require caution. Avoid malls, large crowds. Stick with your tour. Tanzania election violence is in Dar el Salaam....no where near the northern safari circuit. You may have an overnight in Arusha, but it is a smaller town with no need to wander and really, the country politics rarely impacts tourism. You can be 3 blocks from protests or activities, and chances are you wouldn't even know anything was going on. Just follow the advice of avoiding crowds.
Most other months, I would recommend just sticking with Tanzania as there are more animals, and you don't have the border hassles, or changing out travel companies, drivers, vehicles that is fairly common as Kenya and Tanzania do not have reciprocal agreements letting companies do tours in both countries. So, say, Exodus s running a tour of both countries, but it still has to hire a Kenya outfitter for the Kenya part, and a Tanzania outfitter for the Tanzania part. This means the relationship you start to develop with your guides and drivers may not continue in both countries. (i am not aware if this has changed in the past year, but you may want to check this out further if it is important to you).
September generally puts the 'great migration' in the Maasai Mara, so then visiting both countries have some benefit. Otherwise, consider adding the days you would spend in Kenya to a Tanzania trip that goes right up to the Kenya border in Serengeti. This way, you avoid the heightened stress of Nairobi.
So the bottom line is that like any country these events of unrest are isolated and rarely in tourism areas particularly when you are not traveling independently.

The safari compaany we used has offices in both Kenya and Tanzania and so are able to take clients to both countries, with no trouble at the border.

With an established Safari Group, it should not be a problem. There are areas in any country that are you should not visit or venture into.

I went to Kenya last year during the election turmoil and the most I saw were people riding in cars honking their horns. It was also during a time when pastoralists were seizing lodges in the Laikipia area where I would be spending a few days. Noting happened.

I didn’t feel unsafe at any point while I was there.

Thank you. I feel better. We are using Africa Adventure Tours

I would point out that you have to obey your guides. We were told that we COULD NOT walk from the shopping-opportunity to our day-hotel in Nairobi. When we got on the bus to the airport that night, we were told not to open our bus window, no matter how much we wanted the breeze. You're not in charge, the guide is. (Several years ago.)

We stayed one night at the Stanley Hotel in Nairobi, with our safari group. We left the hotel to investigate the area (in broad daylight) and were immediately surrounded and harassed by about five guys. We took refuge in a bookstore and the owner told them to buzz off., which they did. Not a good idea to venture out as we did, at least not in Nairobi.

That doesn’t sound much different than the survey girls in Paris. My whole take on this topic is that people have some unusual fears about Africa. Most people are kind, friendly people who will treat you well just like anywhere else. My experience is limited to Rwanda, but I would travel there again in a heartbeat.

Sorry, Carol, it wasn’t at all like the the petition girls in Paris. These guys were very menacing. I have travelled enough of the world to know when I am in danger. Minaj, our safari leader, scolded us for going out on our own.

While we loved our time in Nairobi, it's not Paris. Follow advice from your guide, hotel staff or other informed person.

Sara,
My husband and I went to Tanzania (including Zanzibar) in February on a safari arranged by Africa Adventure Company and everything went like clockwork. They did an excellent job ensuring we were taken care of every step of the way. We initially signed up for a small group tour but it turned out being just the guide and us with a vehicle all of our own. We were a bit anxious before we went because we had never been to Africa before and now we can't wait to go back. We had an absolutely spectacular adventure! Have a wonderful trip!

The absolute last place I would go for information would be the US State Dept travel Site. (I have great respect for our Diplomatic Corps and think our money would be much better spent on Diplomacy rather than an ever expanding Armed Forces) BUT that site reflects too much political influence and often is written by low level staffers who have little or no experience in the country. It can give a really skewed impression. However it can be at times good but mostly for the real problem areas.

Where you are going will be fine with a tour company.

It is very safe, a friend of mine just came back from Tanzania and he couldn't have been happier.. the safari there is too beautiful, he showed me what he did and the pictures and I'll be going there myself next year (already planned this summer's trips) you'll receive some guidance rules from the guides and in the hotel, like closing windows before leaving and at night because of the monkeys that can steal your things or other things related to safety. they take safety very seriously, so you don't have to worry about a thing.