You can get a good overview of the park in 4 days - enough to make you want to come back for more :-)
I like that you've chosen to stay in the park itself - I feel that it really adds to the experience. However, you do need to make your reservations soon - lodging is limited and will be filling up quickly. I would recommend either Canyon or Lake as the most central choices. Also, staying a night or 2 in the OF area will facilitate viewing the thermal areas. You probably won't be able to get a room at OFI, but Snow Lodge is a good choice in that area and generally has more availability. I'd recommend too that you call Xanterra - don't depend on the website - it's not always up-to-date.
In addition, you may want to post your question on the YNP forum to get more responses - and check out the "Top Questions" in the top right of the forum page - lots of helpful info there.