Where was Urmila the wife of Laxman during the Exile period?

In Valmiki Ramayana, Urmila is not explored much. She was biological daughter of Janaka and she was wedded to Laxmana. Except Shri Ram and Mata Sita, no other couple is explored in the epic properly because it's the story of Shri Ram and his valour. Later retellings gives Urmila some space to be explored. The most realistic scenario can be that she stayed in the palace , did her duties and waited for her husband patiently. The epic doesn't provide the readers any grand reunion between the couple. There isn't a single conversation between Laxmana and Urmila. They both had two sons, Angad and Subahu.

Urmila stayed in the palace of Ayodhya, safe and patiently waiting for her husband. In Mahabharata, Subhadra stayed at the Dwarka with Abhimanyu when Pandavas were in the exile. So, it was something warrior wives often went through because warriors went on wars, many times for a very long period. They were mentally prepared for such scenarios and were emotionally very strong ladies.

In Ramayan’s 14 years of exile, why didn't Ram (and team) go north of Sapt Sindhu? Why did they go south of Ayodhya?

 The Supreme Rama who is dharma personified, did as he was instructed by Mata Kaikeyi.

He started out to dwell in the dandakaranya, literal meaning being “Forest of Punishment”, so called because it is a fearsome unsafe jungle region teeming with rakshasas and wild animals, ever ready and waiting to kill people travelling through the route.

It may be noted that when Raghunatha returned, it was Yudhajita Sahodari who was the most excited, happy and relieved.

After all, she was the one who told and retold countless bedtime stories to the God of Gods.

The relationship between the son and his mother (for Rama, all three Mother Queens were his mother) remained the same, a relationship of great love and affection.

You could go on and on about Shri Rama, what say.

So that is the answer.