Hi there and thanks for your inquiry here,
The are reasonable and budget places to stay close to the airport, there is Mvuli hotel, The strand,West Breeze e.t.c
The hotels so close to the airport are abit expensive but may be worth.
I would not mind to give more helpful info.
Wish hapi travel
I have stayed at Kahama hotel in Nairobi and Mombasa it was less than 40$ clean and safe. Mombasa is a lot better than Nairobi in my opinion and you are closer to Tanzania. Enjoy you trip!
Thanks for all your advices!!!