Hi, yes July is actually a very good time to go to Spiti. Weather is pleasant and roads to all the main destinations are open. I recommend you go via Manali rather than Shimla. Because the Shimla-Spiti route passes through Kinnaur which sees decent rainfall. Landslides due to the rainfall could result in shutdown of roads causing delays. Manali-Kaza highway doesn't see much rainfall thus is the better option.
This is the real peak season in Spiti when the valley welcome hordes of tourists who wish to get respite from city heat. Most of the road links by the mid-June get opened and thus sightseeing in and around Spiti is possible. All the hotel also now offer complete facilities. A visit to Chandra tal can also be made.