How was your day?
Мое утро хорошо. That sounds awkward for naitve Russian ear. If you wanted to say "My morning is good", then it would be better "Сегодня у меня хорошее утро". Using possessive pronouns ("my" here) indicates that your business goes well: your mood is good or you recieved a message from the boss that you don't have to go to your work place today because of wheather but the work day would be payed or something else that made your morning good. There might be any kind of wheather in the morning, that doesn't matter. If you want to say that wheather is beautiful, sun shines, berds sing and a morning is great then don't use possessive pronoun, just say "Сегодня хорошее утро". Notice that I always used the word "сегодня" in both sentences. I think that it is the same in English. Compare: "A morning is good" and "It is good morning today".
Нечего делать. You said "There is nothing to do". That can be but it would be more natural to add some word or words here: "Мне нечего делать", "Сегодня нечего делать". "I have nothing to do", "There is nothing to do today".
Мне хотелось бы поехать в Петербург. That's correct.
Было бы хорошо. That can be, especially if you answer on a someone's question: "Do you want to go to Petersburg?" "That would be good". But if you continue your previous sentence then it would be better to say "Это было бы хорошо". Or just combine both sentences: "Было бы хорошо поехать в Петербург".
Ваше утро хорошо? That's not good. As you were answered before that would be right to ask: "Как прошло ваше утро?", "Как ваше утро?": "How has your morning been?", "How is your morning?". Or: "Do you have a good morning too?" "Ваше утро тоже хорошее?".
How was your day?
Мое утро хорошее(Вы не можете так сказать.. Вы можете сказать "Мое утро прошло хорошо", "Это было хорошее утро"). Нечего делать. Мне хотелось бы поехать в Петербург. Было бы хорошо. Как прошло ваше утро? ("Как ваше утро" - так вы можете сказать в разговорном стиле).
How was your day?
Мое утро хорошеео. Нечего делать. Мне хотелось бы поехать в Ппетербург. Было бы хорошо. Ваше утро хорошеео?
