Yes, President Trump can still run for the office of president again, but the appellate process is not likely to take place before the election. When he is sentenced on July 11th, we will know more about the conditions of his sentence, but none of the sentences are able to change the fact that he is still able to run for the office of president again. If he is sentenced to house arrest, for example, that could hamper his campaign events. Experts have said that it is unlikely that Trump would be incarcerated because this is a first offense which is nonviolent and it's very unlikely for someone with a first offense which is nonviolent to go to prison. But even if he would be incarcerated by this judge, he can still run for the office of president again. So running for the office of president again can not be taken off the table by the court system. It is also possible that the judge could pause President Trump's sentence until the appeals process is exhausted,
Probation is also an option for a first offense that is nonviolent.
Being convicted of a felony (even if temporary due to waiting on appeal and not yet reversed/overturned) does not prohibit a candidate from running for president.
If he does get house arrest, I think we'll see a lot of campaign rallies and other events at Mar-a-lago and at Trump Tower, President Trump's two residences. If there is a probation sentence, then the details of his campaign events will have to be worked out by probation officers in both New York State and Florida.