Some general information about YNP (some points apply to GTNP also)
YNP is about 45 miles E/W and about 65 miles N/S (2.2 mil. Acres total). The figure 8 loop road inside the park is about 140 miles around. The lower loop is 96 miles and the upper loop is 70 miles around and yes, it is bigger than the states of Rhode Island and Delaware combined.
Whatever time that you think you will need to see YNP you better double it, or to say it another way is that you will see one half as much in the allotted time. The Bison think that they own the road (they do!) and will slow down the traffic to walking speed or less for 1/4 mile or more, the thermal attractions also tie up traffic and with a 5 month long summer tourist season that coincides with a 5 month long road construction season and a 45 mph radar controlled speed limit it will take about a full day to see each loop and then you will only see the main attractions. In addition to the occasional construction delays they will also sometimes close whole sections of road (for uninterrupted night construction) between 10 PM and 8 AM in the morning, if you are running late and get caught at night in the wrong area it CAN be a LONG way around to your CG! I don't mean to scare you but to inform you of reality. (The entrance stations will have current construction information or go on line.)
Then there is the elevation- YNP ranges from a low at Mammoth- 6239 ft to 7784 ft at Fishing Bridge or higher if you go hiking! Drink plenty of liquids and pace yourself when walking. And again I don't mean to scare you but rather to inform you, after all there was 4.1 million visitors in 2015 (record number)
I recommend that you get up EARLY, leave the CG and be back by 4 or 6 PM have dinner and be sitting in your recliner drinking a cool one when your neighbor drags himself back to the CG at 8-10 PM. Remember that from mid May to mid July in YNP the sun doesn't set until shortly before 10 PM.
Clothing- Especially in the early or late season it is not unusual to have a 30 or even the occasional 40 degree temperature change throughout the day. Dress with easily shed layers of clothing. Also dress in bright easily seen clothing. I am sure that we all have been to a sporting event, parade or Disney World etc. and we blink our eyes and our partner/child has disappeared. My DIL was born and raised in HI, you guessed it, every Xmas, b-day or Father's Day I receive a Hawaiian shirt. One of them is black with 4-5 inch dia. bright flowers. Not many of them in Wyoming and in YSNP, that is what I wear. If your partner has on a Violet blouse and a Orange scarf with a Pink hat I guarantee that she will be the only one within the boundaries of either NP. It can save you a few anxious moments.
Water- Now I will have to contradict myself, at the altitude of YSNP yes, drink lots of water!HOWEVER, be aware that the flush toilet restrooms are are in the major tourist areas- Mammoth, Canyon, Fishing Bridge, Lake Hotel, Bridge Bay, Grant Village, Old Faithful, Madison Junction etc. The geyser basins and other thermal attractions areas have only pit toilets. I have seen the pit toilet line at the lower Geyser Basin 25 or more feet long (bless the tour busses) So be smart about drinking your water and use the major tourist area R/Rs before leaving the area!
Sun- At YSNPs altitude the sun is intense (uv) have and apply sun screen, wear that old floppy wide brim sun hat, wear sun glasses!
If your luck is like mine Old Faithful will have just erupted when you get there and you will have a hour and 10-20 minutes wait for the next one. Tour the O/F geyser basin while waiting for the next eruption. Old Faithful INN is a must see (meals are "OK" also)
We have lived about 110 miles (4739' elevation) from W. Yellowstone, MT since 1964, go there 3-4 times a summer (normally before Memorial Day and after Labor Day) and haven't seen it all of it yet!
When in the Jackson area I highly recommend seeing the Bar J Chuckwagon dinner show! If you go, MAKE RESERVATIONS and BE THERE EARLY TO PICK UP YOUR MEAL TICKETS/SEATING ASSIGNMENTS! They seat you by when you show up to get your tickets NOT by your reservation number. Tim, their fiddle player has won the "Idaho state old time fiddle contest 7 times and the US open fiddle contest twice". We day trip it there 2-4 times every summer to see them! Disclaimer- We have no financial or other interest in the Bar J only that it will be the best $$ value for your money for your trip! Check out their website.
Bar J Chuckwagon