I have messaged the OP.
The Darjeeling - Sikkim circuit is a very popular circuit. Travel is safe especially for women and the place abounds in scenic beauty ( in spite of the heavy tourist traffic and ham handed attempts to increase tourism infrastructure by building grotesque , concrete monstrosities and by damming up the river and pockmarking the hills with tunnels etc). Here is a brief lowdown on the various places you can visit.
Darjeeling - still beautiful but very crowded. Don’t forget to visit HMI , the zoo ( probably the best small zoo in the country and the red pandas are cute) and the Happy Valley tea garden. I don’t think it’s a big deal but people like to do very hill station things like strolling in the Mall , English breakfast at Keventers etc, Glenary’s cakes etc. The DHR is overrated but since you are here it’s a good photo op.
Kalimpong - It’s a well known for its flowers , unhurried pace of life , good weather and scenic beauty. Less well known than Darjeeling ( thankfully) but charming and idyllic in its own way.
Kalimpong town itself is over crowded and over populated with vehicles. I would give it a miss or just a few hours.
Both Kalimpong and Darjeeling have a certain colonial legacy . Almost all houses have gardens, speak English passably , are ecumenical , have some musical talent ( yours truly being a rare exception) ,take special attention towards a more westernized attitude towards grooming etc. People are generally friendly and women are treated well and have a very high standing in society and take up vocations ( like bar tending or waiting in booze serving restaurants without it appearing like an aberration ) which may be quite incongruous in other places ( I would be happy to be proved wrong). Single women , even young ones can travel alone without facing any harassment or stress. Kalimpong has some good souvenirs like thankas, other type of paintings , handicraft bags to carry home as gifts.
Downside : Folks sleep by 7/8 so unless your hotel has some special nocturnal events planned , forget about a nightlife.
The Himalayan mountain ranges are spread panoramically and the greenery and diversity is immense.
Sikkim is a linguistic, geographical and cultural continuation of Darjeeling but better administered and therefore cleaner and more swanky.
West Sikkim - my favorite. Very scenic. You can see the Kanchenjunga masiff from very up close from places like Pelling and Ravang. Mountains , lakes , waterfalls , there works .. of nature. Rich in history too with old palaces forts and monasteries and not given much to the vagaries of the weather like North Sikkim.
North Sikkim : rugged , beautiful , mountains , lakes , glaciers but a little prone to slides etc.
East Sikkim : has Gangtok with its glitzy shops , MG maarg ,a kind of promenade with some cultural happening or the other most of the times , and of course for the high rollers , casinoes.
The East also has the popular silk route circuit with the tortuous meandering of the road leading to the Jelep La pass.
One thing about Gangtok , it’s clean and the pedestrians are respected with good walkways all around town.
Trek
Not sure it’s recommended to the OP with the small kids.
But Sandakphu and Phalut is a good easy trek. On a clear day .. when you can see forever .. you can see Everest and Kanchenjunga together. Octobers are clearer with the monsoons washing the dust and haze. April is full of rhododendron blooms but cyclonic showers and hailstorms might cause a bit of alarm.
It’s the best trek this side of the Annapurna.
The HMI has adventure, basic and advance mountaineering programs. The Dzongri trek in West Sikkim is also popular but may need reasonable fitness and a tolerance of the low oxygen air of high altitudes.