to run this way and that (idiom); to rush about busily
to bustle about
to hopscotch
also 東跑西顛|东跑西颠[dong1 pao3 xi1 dian1]
Definitions (Wiktionary)
phrase, idiomatic
to rush about busily; to busy oneself; to run about; to be on the move
Definitions (HSK3.0)
HSK3 七一九级词汇表 #906
Examples (Tatoeba—Mandarin-English)
Mandarin
长年累月东奔西走忙死了，生活太没有规律了。
長年累月東奔西走忙死了，生活太沒有規律了。
cháng nián lěi yuè dōng bēn xī zǒu máng sǐ le ， shēng huó tài méi yǒu guī lǜ le 。
I'm so busy running about year in, year out. My life has no consistency.
Examples (Wiktionary)
Mandarin
如今的旧友中，把裤腰带上别一电蛐蛐，整天东奔西走，蒙吃蒙喝，招摇过市的浅陋之徒越来越多了，而如祥明这么赤诚执著的人，却已是凤毛麟角，也许正由于此，我反而格外地敬重这位城市里的庄户人，我觉得修祥明永远是富有的，这除了他的乡土经历、他的朋友之外，还因为他拥有文学。
如今的舊友中，把褲腰帶上別一電蛐蛐，整天東奔西走，蒙吃蒙喝，招搖過市的淺陋之徒越來越多了，而如祥明這麼赤誠執著的人，卻已是鳳毛麟角，也許正由於此，我反而格外地敬重這位城市裏的莊户人，我覺得修祥明永遠是富有的，這除了他的鄉土經歷、他的朋友之外，還因為他擁有文學。
rú jīn de jiù yǒu zhōng ， bǎ kù yāo dài shang bié yī diàn qū qu ， zhěng tiān dōng bēn xī zǒu ， mēng chī mēng hē ， zhāo yáo guò shì de qiǎn lòu zhī tú yuè lái yuè duō le ， ér rú xiáng míng zhè me chì chéng zhí zhuó de rén ， què yǐ shì fèng máo lín jiǎo ， yě xǔ zhèng yóu yú cǐ ， wǒ fǎ né r5 gé wài de jìng zhòng zhè wèi chéng shì lǐ de zhuāng hù rén ， wǒ jué de xiū xiáng míng yǒng yuǎn shì fù yǒu de ， zhè chú le tā de xiāng tǔ jīng lì ， tā de péng you zhī wài ， hái yīn wèi tā yōng yǒu wén xué ．
Among my old friends now, there are more and more of these shallow people who have beepers clipped onto their belts, running about all day, cheating their way, and act ostentatiously in public, yet people who are as sincere and persistent as Xiangming are very rare. Perhaps exactly because of this, I actually particularly respect this farmer in the city. I think that Xiu Xiangming is forever rich; other than his experiences in his hometown and his friends, it is also because he has literature.