I will be visiting Beijing in April for 8 days· What is the weather like around this time of the year?

According to the weather records in the past, it will get warm and pleasant in April in the city, with the average temperature of around 14C. As there will be large temperature gap between daytime and nighttime, you'd better take a windbreaker or overcoat in case.
And eight days are definately enough to explore the city. If you are interested, I suggest you visit some places around as well like Tianjin.