You may find the Bible's answer to your question somewhat startling–because it tells us to pray all the time! It says, "Pray without ceasing" (1 Thessalonians 5:17, KJV). Paul wrote to the Christians in Rome, "Constantly I remember you in my prayers at all times" (Romans 1:9-10).
Behind this is a simple but important truth: We can come to God at any time, because He wants our fellowship. God doesn't keep office hours! And He also welcomes us because He knows we need Him, and He wants to help us. No situation is beyond His concern, because He loves us and wants what is best for us. Prayer is not an obligation but an opportunity–an opportunity for us to grow closer to God and seek His will for our lives.
Does this mean God wants us to lock ourselves in our rooms 24 hours a day, with our eyes closed and our lips constantly moving in prayer? No, this isn't what He commands. Instead, He wants us to cultivate the habit of quietly praying in our souls about everything throughout the day. Even when you are talking with someone, you can be praying for them in your spirit.
Special times of prayer are important; I commend you for wanting to start each day with prayer. But ask God to help you turn to Him in prayer all day long also–not just praying about your needs or the needs of others, but also praising and thanking Him for all He has done for us in Jesus Christ.