travel in Kyoto

I plan to travel Kyoto with my family -3 together in the end of May. How is the weather in May? Is hot spring popular in Kyoto? What is the average rate to book a traditional Japanese lodging? Is it easy traveling in Kyoto by public transportation?

Thanks.

Here are weather basics (Kyoto is just next to Osaka):
http://www.japan-guide.com/e/e2273.html

Is hot spring popular in Kyoto?

There are some, but it is not the most outstanding prefecture for hot springs. The city itself has some artificially bored ones in the outskirts. Among them my favorite is the Kurama rotemburo:
http://www.japan-guide.com/e/e3933.html

If you want to visit a hot spring in the region, you should also consider Arima:
http://www.japan-guide.com/e/e3558.html

And more distant Kinosaki:
http://www.japan-guide.com/e/e3525.html

What is the average rate to book a traditional Japanese lodging?

15,000 yen per person including two meals. Of course there are many lodgings that are cheaper and more expensive. But 15,000 yen is about average. More details are here:
http://www.japan-guide.com/e/e2029.html

Is it easy traveling in Kyoto by public transportation?

Kyoto does not have the most convenient network of public transportation, but it is still easy to get around. The basics are introduced in the second half of the following page:
http://www.japan-guide.com/e/e2363.html