Hi and congratulations on getting married! :)
If you have time it is better to have at least 2, possibly 3 nights safari. From the South Coast you can do a road trip to Tsavo (East and West) and time permitting, even Amboseli, although it is a little far and probably requires some extra time to enjoy. I think one night safari is a bit too much driving to and from, rather than actual game drives. Although some people do a day trip to Tsavo East, but it is not my cup of tea :) I like to take time on safari.
If you specify to your operator that your are just 2 of you, you should get a quote based on exclusive use of vehicle. Usually it will be the case as what are the chances that someone else would like to do the same over the same days with this particular operator? Sharing a vehicle is usually the case if you are joining a group safari with pre-arranged itinerary. And definitely your own vehicle is an advantage as you will be in control of how long you want to spend on watching elephants or lions :)
You can also travel to Masai Mara, but there you are looking at flying to and from - too far from the coast. It will be a more expensive option but if budget permits, totally worth it. There you have to find out if you have to share a vehicle or perhaps can pay extra for exclusive use as game drives will be by a lodge vehicle.
Also, once at the coast, you can have a much shorter trip: combine a trip to Shimba Hills National Reserve with visiting Mwaluganje Elephant Sanctuary - 40-60 min from the South Coast resorts. For both you will need a day and can have a picnic lunch or lunch in a lodge in Shimba Hills. For Shimba Hills alone you will need an afternoon: leave after lunch and you will be back by dinner. Make a special even of it - champagne sundowners at the viewing point at Shimba Hills! Shimba is a small park, entry fee is still USD 20 per person and it is the only place where you will see sable antelope in East Afrcia. There are also elephants (smaller and grey, unlike elsewhere), giraffes (there are 3 of them, they are not native to this park), buffaloes, antelopes, warthogs, etc.
Have fun planning and enjoy your trip!
Tijara Beach Hotel