I lived in Baguio for almost a year and even now I still miss the cool breeze and beautiful sites. Living in Manila is way different from Baguio. Both are city but obviously Manila is more developed , although Baguio has establishments and restaurants already,  so if you want to live in a province like place with cool weather this is my no. 1 recommendation for you, specially if you grew up in Manila. If you are just a tourist I can say that Almost everything you're looking for is  here.
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SESSION ROAD
You will find this place in the city proper itself. You will see restaurants, malls, boutiques and ukay ukay shops along this steep road. On week ends at around 9pm you will find night market here but it would depend because the government doesn't approve the idea and forcing the vendors to leave. But if your lucky you'll see this night market, and it will surprise you with its price. You can buy a proven signature clothes for 10 pesos and above and for new clothes price is from 50pesos and up. You can also find toys, shoes and likes for an affordable price. You can also find restaurants that you can only find in Baguio such as Volante and Zola. But be sure to wear a comfortable pair of shoes when you go here because the road is really steep you might sprain your ankle/legs if you will wear high heels specially if you're not familiar with this road. And if you can, avoid walking alone, for at night there are gang wars  happening in this area, but police here are quick and is patrolling every now and then.

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BURNHAM PARK
I think this is the most popular place in Baguio because of the different things you can do here with your friends and family. You can rent a boat and bicycle, have picnics or shop for souvenirs. You can see different flowers here that you wont see  in Manila because of the weather. Once or twice a year they host a Landscape contest and I promise you wont get bored because of the different designs and colorful flowers. And on summer there's bazaar which you can play, shop and eat, entrance fee if still the same is 15 pesos per head.

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NEVADA SQUARE
I've been here a few times,  I can say that if you're into party and "gimiks" this is the beast place to go. There are atleast 10-15 Bars here, restaurants and karinderia's. But my favorite is the barbeque stall because of the barbeque dried squid. This place is quite the same like what we have here in Manila, So if your on vacation and bored you can visit this place. But just a reminder there's a Curfew in Baguio for children/teens age 17 and below which starts at 7pm til 5 am.

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SM Baguio
You know this Mall if you grew up here in the Philippines. Owned by Henry Sy and you'll see this mall almost everywhere. The difference from this branch with others is that its an open Mall it doesn't have Air-conditioning system, but because of Baguio's weather you will still need your jacket in this place. The location is just above session road and since its sitting on a  high ground the wind is more colder. At the highest floor you can find a public binocular which you can use for 3 minutes by dropping 5pesos. This Place has the most spectacular view in Baguio, having coffee at night here is a must.

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Mines View Park
This is around 30 to 45 minutes away from the city proper but I love going to this place because of the food and souvenirs but aside from that, the spectacular view is the main reason why tourist go here. You will see the best view of the mountains from this place. While doing sight seeing you can also toss coins in the cliff and native Igorot will catch it while jumping and standing in the cliff side which is cool and scary at the same time. Have some pictures with horses or while wearing Igorot clothes. Here you can also find Good Shepherd Convent where you can buy the famous and the most delicious ube made by Nuns.  Just be there before 3pm because they only have limited stocks, but there's limitation in buying per person for they only make small quantity of ube everyday, they made that rule to give way for others. Just make sure to go to the bathroom before you go here because you have to pay 5 pesos entrance and their rest room is traditional, it doesn't have a toilet bowl.

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CAMP JOHN HAY
If your looking for signature clothes and want to play golf, this is the place for you. Here you will find the most popular Manor Hotel which has 18 hole golf course. And here you will also find Nike boutique, Adidas and likes that offer factory priced items. You can also check out the Bell Amphitheater, Igorot Garden, Mermaid Garden,The Lost Cemetery, Butterfly Sanctuary and the Art Park. And after your tour you can relax in the famous Chocola-te de Batirol shop and taste their famous hot chocolate.