Yellowstone National Park covers a huge area and if you plan on having a good amount of time to fish any one stream, you need to be located in a campground or town around the perimeter of the park close to that stream, otherwise, you may need to spend much of the day traveling from back and forth from your base location to the particular stream you plan on fishing. There is always some general variation in the weather from year to year as well as variations in the snowpack which controls the amount of water in most of the streams. Changes in the weather from day to day is common and completely unpredictable very far in advance. I am basing this on the typical or average weather conditions we have experienced during the years we have been fishing in the park.
During the month of June, you were limited to a rather few streams that had warm enough water to fish for trout. By July, many other streams in the park and upper sections of the Firehole, Gibbons become warm enough to fish. The Madison inside the park will begin to get a little too warm during the first part of July. The northeast section of the park including the Lamar, Soda Butte and Slough Creek can be warm enough to fish but you always have to check the stream flow data to know for sure. If the streams are low and clear enough during the first part of June, it will be a great place to catch lots of trout.
The Gallatin River inside the park is always a popular spot to fish the first part of July. July is also the heart of the tourist season and West Yellowstone can be crowded. The Gallatin is easily accessed from there. It can be counted on for good opportunity but can be crowded in spots at times.
The Gardner River is always a good option especially for those staying near the northwestern section of the park. The first part of July can be a little crowed with tourist in this section of the park as well. All sections of the Gardner are usually in good shape during the first two weeks of July.
Lower sections of the Yellowstone River are always a good choice for the first part of July. Much of this section requires some hiking to reach but not all of it. At least that gives those willing to go to a little effort hiking an opportunity to get away from the tourist and the easy accessed crowded rivers and streams. The upper section of the Yellowstone River above the Chittenden Bridge doesn’t open until July 15.
The Snake River and its tributaries within the park located in the southern part of the park can fish well during the first part of July but most of it requires some hiking to reach. Of course, that is a good way to get away from the large tourist crowds. The Belcher and Fall Rivers located in the southwestern section of the park can be okay near the middle of July but don’t count on it.